After four years of trying to fashion foreign policy with one eye on his reelection and another on the struggling U.S. economy, Obama is now liberated on both fronts.

A decisive win in the Electoral College means he doesn’t have to worry as much about his daily approval ratings. And as the economy slowly improves, the optics of foreign travel aren’t as bad. On Thursday — two days after his reelection — the White House announced Obama will leave for Asia next week, embarking on a four-day, history-making trip to Cambodia, Myanmar and Thailand.

( Also on POLITICO: 5 key decisions for President Obama)

Of course, the challenges abroad look daunting: Iran’s nuclear program threatens, the Arab Spring seems to have unleashed chaos across the Mideast and Al Qaeda is metastasizing. But for any reelected president, the notion of a foreign policy legacy has a certain allure. It offers a chance to leave a lasting global imprint — and an alternative to the daily interference of Congress on domestic issues.

“The second term is the term that will determine whether [Obama] will be a historic president — beyond the fact that he’s a historic president by virtue of who he is,” said Zbigniew Brzezinski, President Jimmy Carter’s national security adviser. “Beyond his DNA, we need some international accomplishment that really is historically transformative, and so far we haven’t had any.”

Here’s a look at six foreign policy areas where Obama might do things differently in his second four years:

Iran

Tehran’s nuclear program is the administration’s biggest foreign policy problem.

( Also on POLITICO: Obama administration announces new Iran sanctions)

The Pentagon’s announcement Thursday that Iran tried to shoot down a U.S. surveillance drone showed just how tense relations are between the U.S. and the Islamic Republic.

In the final days of the campaign, the White House tried to knock down a report in The New York Times that direct U.S.-Iranian talks on the nuclear threat are likely to start soon, but nearly all experts expect such a dialogue to get under way shortly.

“I think the administration is quite likely to try to find a way to direct diplomacy with the Iranians and to interest the Iranians with a big proposal rather than an incremental proposal,” said Robert Satloff of the Washington Institute for Near East Policy. “There may not be such a [diplomatic] solution, but I think they will exhaust the effort to try to find out.”

Those kinds of talks would alarm foreign policy hawks and some advocates for Israel, who fear Obama would make an ill-advised deal in order to fashion a legacy. The same conservative critics who believed that Obama made an international “apology tour” soon after taking office now worry he’ll embark on a “concession tour,” trading away U.S. military leverage and superiority to ink flimsy pacts with rogue nations such as Iran and other U.S. adversaries.

“When you’re dealing with a country that can operate secretively and in bad faith, these deals are not very valuable, but given past history you have to think that that rather ineffective course may look attractive to the administration,” said Doug Feith, a fellow at the Hudson Institute and an undersecretary of defense under President George W. Bush.

“Before the election, a deal like that would have gotten intense political scrutiny. It probably wouldn’t have looked very good. It would have been risky, but now that [Obama] has got four more years, there may be people [in the administration] who think if we’re negotiating a deal like that. … it might make it much harder for the Israelis to act,” Feith said.

Less-hawkish analysts also believe Obama would be more open to a deal with the Iranians now, even if it makes Israel’s government uncomfortable.

“I think he would, and the election is part of it and the movement we’ve seen from Iran [because of sanctions] is part of it,” said Hussein Ibish, a prominent Arab-American commentator. “If you go into an election saying, ‘I’m about to sign a deal with Iran,’ that can be heavily criticized by whoever, be it the prime minister of Israel or any Republican or any hawk or anybody who doesn’t trust the Iranians.”

At the foreign policy debate last month, Obama said the door was open to diplomacy, but U.S. patience had its limits.

“There is a deal to be had, and that is that they abide by the rules that have already been established,” Obama said. “The clock is ticking. We’re not going to allow Iran to perpetually engage in negotiations that lead nowhere.”

The Afghanistan slope

While all eyes are on the fiscal cliff, Obama faces an imminent decision on what could be called the “Afghanistan slope”: the pace at which U.S. troops will be withdrawn between now and the end of 2014.

The top U.S. commander in Afghanistan, Gen. John Allen, is set to deliver a report this month making recommendations on how many of the 68,000 American forces in the country should be pulled out and when.

The American public is clearly weary of the war, but the schedule for withdrawing is almost purely a commander in chief decision.

Obama “can pretty much do what he wants,” said Michael O’Hanlon of the Brookings Institution. He expects Allen to offer Obama about four options, including a slight decrease to perhaps 60,000 troops, a cut to perhaps 25,000 troops and a dramatic drop to something like 15,000 troops. “Obama insists on being given options. He’s not just going to let Allen give his recommendation by itself.”

The biggest constraint on Obama on this decision may be his own rhetoric. He’s said publicly that withdrawal will continue “at a steady pace” through 2014, a pledge that would seem to be at odds with still having 60,000 or 50,000 troops there by the end of next year.

“He did say that, but I sort of hope he forgets it. I don’t know that they really feel locked in by that,” said O’Hanlon, who favors keeping a robust U.S. military presence during the transition to Afghan security control. He noted that Obama pledged a rapid withdrawal from Iraq and later backed away from that. “He gave commanders a lot of leeway.”

Syria

The ongoing bloodshed there is one of the world’s most glaring crises, but the U.S. has thus far played a limited role.

Some who favor more assertive U.S. involvement hope Obama will strengthen his response now that it’s less likely to be seen as capitulating to Republican criticism or “mission creep” that could result in dangerous weapons falling into the hands of Al Qaeda.

“We’ve had a policy that until now looks like the subject of drift. It’s starting to look like a lack of leadership. People are calling it apathetic and indecisive, which I think is too harsh, but people in the region are getting that impression,” Ibish said. He said Obama could feel freer now to take some “nuanced” steps — not introducing U.S. troops but perhaps providing U.S. weapons directly to moderate elements in the Syrian resistance.

“I think this is the area most likely to see the quickest change,” Satloff said, predicting a move toward the U.S. giving “lethal weaponry” to the Syrian opposition.

Mideast peace

Many U.S. presidents have been tantalized by the idea of solving the Israeli-Palestinian conflict, so it would seem like a logical target for Obama in his second term save for one thing: He failed rather dramatically at it during his first.

“He’s not going to roll this rock up a hill 100 times if there’s no receptivity among Israelis or Palestinians,” said former Mideast peace negotiator Aaron David Miller, now with the Woodrow Wilson Center. “You can’t press against a wall.”

Some pro-Israel activists worry that Obama, free of concern about reelection, might try to force Israel into some kind of deal, but others say the president is unlikely to do anything that would anger Israel’s numerous allies in Congress.

“The president doesn’t operate totally divorced from politics and the rest of the political system,” said Josh Block, a former spokesman for the American Israel Public Affairs Committee.

Brzezinski put the question of Mideast peace in stark terms: “We have to decide if it’s in our national interest for it to be resolved, or isn’t it? If we’re indifferent, so be it, but our indifference in a way may result in the eventual destruction of Israel.”

The Israeli-Palestinian conflict seems likely to be on the back burner until the Iran nuclear issue is settled, but a trip to Israel by Obama seems probable in the coming months, if only to make up for the absence of such a trip during his first four years in office.

Arab Spring

A likely Obama visit to Israel raises an intriguing question: Where else would the president go on such a trip?

Presumably, he’d visit with Palestinian leaders. And many experts also believe a stop in one of the Gulf states could advance the idea that Iran’s nuclear program is a threat to the whole region, not just Israel. But visiting one of the undemocratic Gulf countries would raise questions about whether Obama’s support for the Arab Spring democracy movement is just rhetorical.

So, a stop in a country being transformed by the Arab Spring might be useful, but which one? Egypt is by far the most pivotal, but the optics of Obama meeting with its Islamist government could underscore fears that democracy in the region will lead to theocracy. “A handshake with [Egyptian President Mohammed] Morsi against the backdrop of the Muslim Brotherhood might not be what the White House wants,” Miller said.

“There’s a strong argument for going to Egypt, but obviously that’s very problematic to be hosted by the Muslim Brotherhood government before we have really clear picture of how they’re going to develop. That’s a problem and a risk,” Feith added.

A more likely Arab Spring stop: Tunisia, where the movement began.

And if Obama really wanted to be edgy, he could do a quick stop in Libya. His security team wouldn’t be happy, but it could boost Libya’s fledgling democracy and send a message that the region is not awash in anti-American anger.

Russia

Russia is the area where foreign-policy hawks have their best evidence that Obama might go wobbly.

In March, he told outgoing Russian President Dmitry Medvedev that Russian objections to a U.S.-backed missile defense plan could be resolved in Obama’s second term.

“This is my last election,” Obama said in a conversation he apparently didn’t realize was being picked up by media microphones. “After my election, I have more flexibility.”

“I understand. I transmit this information to Vladimir,” Medvedev responded, referring to Russian leader Vladimir Putin, who recently resumed the presidency.

In an interview last month, Obama portrayed his remark as innocuous. “The discussion there very much just had to do with the fact that it’s hard to negotiate additional treaties when I’m off campaigning and doing all kinds of stuff,” he told KRNV-TV in Reno.

Obama, who’s eager to reach an agreement that further reduces U.S. and Russian stocks of nuclear weapons, is clearly willing to make concessions to accommodate Russian concerns about missile defense.

But his high-profile statement to Medvedev may have narrowed the administration’s options. The Senate would have to ratify an arms treaty with Russia, and Obama’s awkward soundbite will ensure that any missile-defense trade-off with Russia gets ample attention.

For all of Obama’s foreign policy leeway, Congress can still make its will felt on national security matters.

And the broad constraints on U.S. power abroad are real. The country’s $15 trillion debt and the political pressure to get it under control means anything with a significant price tag faces an uphill battle — and could restrict Obama’s foreign policy legacy.