Serious Prediction: LeBron remains in Cleveland.
My bullshit, sitting-on-the-couch, psychological analysis of LeBron James is that he is an egomaniac, but an intelligent egomaniac. I imagine few things are more enjoyable for an egomaniac than being the center of a year long media circus, and this media circus has reached the Gunther Geble-Williams segment of the show. Everybody is watching now.
If LeBron was entirely motivated by ego, however, I would be predicting he will sign with Los Angeles, New York, or Chicago. What better way to satisfy an ego of otherworldly size than to take on Kobe in L.A., Jordan's legacy in Chicago, or the entire media world in New York?
But, my guess is that LeBron is too smart to try any of those feats.
First, the talent level on the mentioned teams is only marginally better than Cleveland, if not drastically worse. Chicago has a great young player in Derrick Rose, but we're not talking about LeBron teaming with Shaq or Duncan (or even Dwight Howard) in their respective primes. LeBron going to New Jersey to play with Devin Harris and Brook Lopez or the Knicks with Stoudamire (a knee/eye injury waiting to happen) and the promise of Carmelo maybe/hopefully next year? Sorry, he is too smart for any of that.
Second, no matter what anyone says about money not being a real factor, because LeBron or any of the other marquee free agents can make up the less-than-max contract which can be offered by the suitor (non-home) teams, with other lucrative perks... the money is still a huge factor. As I understand it, Cleveland can offer 6 years, $126 million, everyone else can offer 5 years, $96 million. To leave the home team, you basically have to be willing to give up a guaranteed $30 million.
Chris Bosh has already said he won't, and will probably be part of a sign-and-trade. A'mare Stoudamire took less, but only because the Suns wouldn't give his busted retina/knee microfractured ass more than 3 years. D-Wade can talk about taking less, but all signs point to him staying in Miami (and convieniently, recruting others to take less). Joe Johnson already took the money. These guys can talk all day about taking less to play together, but as of right now, they have taken exactly $0.0 million less than the max they could receive. LeBron is not going to be the goof making less guaranteed money than Joe Johnson or Chris Bosh.
Finally, LeBron is smart enough to know that he rules the roost in Cleveland. Could LeBron and his high school pallies (aka as his "management team") have the same free reign in any of the big media markets? Probably. But, if he is smart, he'll know the scrutiny will be alot greater, and the consequences alot more painful in NYC or Chicago or L.A. Basically, LeBron and his buddies have the run of the franchise and the city in Cleveland, because it's literally (OK, not literally) possible that Cleveland cannot survive without him. In Chicago, he is immediately -6 in comparison to Jordan, in L.A. he is -5 to Kobe, while NYC will give him exactly one honeymoon season of love before they simply expect one championship... every season.
LeBron is too smart to fall into any of these traps. His ego loves the circus and the attention, but in the end he'll stay home.
LeBron is less smart than I think: Knicks
David Stern conspiracy prediction (i.e. something something New York something media control something Patrick Ewing lottery something): Knicks
11 year-old Matt Brennan's dream fantasy prediction: Harlem Globetrotters ("LeBron will play in Pittsburgh every year right after Christmas!!! Hey, look out! LeBron is going to throw water in a bucket on the front row!!! Wait... it's just confetti!!!!)