I remember when he dropped out, there was a lot of talk that he'd try to parlay his endorsement into the Attorney General's job or Labor Secretary or maybe even the number two spot on the ticket (again). Of course, Edwards himself has said that he only dropped out after securing Obama and Hillary's promise that they'd make poverty a priority--so, presumably, he'd be inclined to endorse the candidate who made it a bigger priority. But no one really believes that. Except, maybe, for me.
Given Elizabeth's health, and the fact that he's got his (much-mocked) dream house in North Carolina, would Edwards really want to take a cabinet position that would move him to Washington? I could see him being willing and eager to go to Washington as president, but I'm not sure he'd want to do it for any other job. In other words, maybe Edwards's endorsement decision is being governed by idealistic motives.
As for what Edwards does next beyond the more immediate question of his endorsement, I'm assuming he's going to want to do it in North Carolina. Which doesn't give him that many options. It's too late for him to get into this year's gubernatorial race. And, like I said above, I don't see him wanting to return to Washington for anything less than the White House, which would rule out his returning to the Senate. So here's my idea: He should become the chancellor of the University of North Carolina--which, conveniently enough, is a job that's currently open.
Becoming a university president would certainly be a counterintuitive move on Edwards's part; but it would give him a public platform, and if he used that platform to continue to talk about poverty (and worked to make UNC a leader among educational insitutions in dealing with that issue), it would be a very impressive and admirable thing. And it would certainly be idealistic. He'd also probably get some pretty choice seats to watch Carolina basketball. What more could he want?