If you don't mind the handling, I'd go D7100, too. Especially if you like to shoot sports.
That said, I went from a D90 (very similar handling to the D600/D7100) to a D300s and I'm never going back. In fact, if there is ever a D400 or I move to FF to a D800, I'm going to have to spend some real time seeing if the updates to accommodate video (which I don't care about) are a backward step or not for how I shoot. I really love the handling of the D300s, and for that reason alone I'll probably wind up with a D700 at some point (although I lust for a D3s).
Thanks everyone for the advice here. DX is not interesting to me... it doesn't offer the perspective or look that I want to achieve, and I already have a pair of D7000 bodies at work that I can borrow.
OK, so I tried the D600 out, and I have to say I'm impressed with it. Quite impressed with it. The RAW files allow for a TON of dynamic range - DR the likes of which I haven't seen since film!
I think I can live with the button placement of the D600 too...
QUESTIONS FOR D600 OWNERS/USERS:
My main goal is to use this for street candids, and also to tinker with and become better at flash photography with speedlight-based setups, and the D600 is a 1/2 stop slower than the D700 - which is a lot of ambient light control... though the D600's base ISO is 100. Anyone hitting any major limitations there?
The conditions I was able to test the D600 under were very bright - any of you D600 folks NOT happy with the low-light focusing performance? I've heard good things from local photographers with their main/only criticism of it being the small coverage area in the viewfinder.
You know what you've got with the D700, you can always try the D600...if you don't like it there is a good market for a used body and you'll have enough money for the D700. For me, I don't think I'd consider the D600 anything more than a second body, but it's all pretty much personal preference. I've also seen some pretty good deals popping up from time to time on D700, so if you wait it out after getting a D600 a second option might come along.