It's fun to speculate about who the next chair of the Federal Reserve will be (Wonkblog, Economist), but let's be honest—it'll be Janet Yellen. The only other realistic possibility is that Ben Bernanke will reluctantly (or perhaps "reluctantly") agree to a second tour of duty.
But if Bernanke steps down as expected, then you'd need a very compelling reason to pass over the clearly best qualified candidate. When that candidate would also be the first woman to hold the job ever, you're talking about a pretty high bar. Pass over Yellen to tap Larry Summers? For what purpose? I think the Stanley Fischer option would be fun, and if it were up to me, I would bring in an outsider dedicated to "regime change" such as Christina Romer. But there's been zero indication that at any point in his political career Barack Obama has given a moment's notice to the idea that innovative thinking on monetary policy should be part of his legacy. So it's Yellen, Yellen, Yellen, Yellen, Yellen.
Who is Janet Yellen? She's currently the vice chair of the Federal Reserve. Before that she was president of the San Francisco Federal Reserve. She's a Democrat. For the past decade, she's been a monetary policy "dove." She was an advocate for the Evans Rule on the Federal Open Market Committee. She's familiar with the importance of nominal income expectations. In other words, a good choice on the merits as well as the obvious choice in terms of credentials and a historic choice in terms of gender. For a president with no particular interest in pushing the envelop on monetary policy, it's a no-brainer.
The interesting question is how much of a fight Senate Republicans will put up when she's nominated. She's a proponent of both fiscal and monetary stimulus, so they won't like her. And they'll have the votes to block her. The brave new world of filibustering everything all the time has yet to be put to the test when it comes to mission-critical jobs like Federal Reserve chair and Supreme Court justice, but the ratchet keeps moving on this stuff.