If LeBron wants to win multiple championships, he would sign with Oklahoma City. A team with Durant, Westbrook, James, et al. would be a dominant force over the next 5-10 years.
Of course, there's not a chance in hell that he signs with OKC. In the end, I think he will sign with the Bulls to play with Derrick Rose and Joakim Noah. If they could somehow find a taker for Luol Deng's albatross of a contract, then the Bulls could probably fit in a second max contract and make it even more enticing for LeBron.
I don't see LeBron signing with the Knicks. The Knicks should have enough cap room to sign two max free agents, but I don't believe that they have the supporting cast necessary to compete for a title immediately. Wilson Chandler and Danilo Gallinari are nice players, but not nearly as good as what a team such as Chicago or Miami (or even New Jersey) can offer.
Personally, I hope he re-signs in Cleveland. However, for myriad reasons, I don't think that will happen.