Probably the 17-35, but it depends on your style of shooting. Most street photographers tend to shoot a little short, or a little long. I personally like my lenses a little long, and on a 1.5x camera like yours, a fast 50mm would give me about a 75mm FOV, which is close to perfect (for me.)
For street photographers who prefer things a little wide, the 17-35 is a terrific lens (equiv. FOV of ~25-52), but it *is* large and heavy. I have it and I find that it seems to balance better on larger cameras, like the D2x or D3 -- your D200 body is only a couple of ounces heavier than the lens. That's mostly a thing of getting used to it, but you should definitely try it out first. It's *heavy* if you carry it all the time -- more than three pounds for lens and body together.
If you have not yet worked out how you like to shoot (long or short), then a zoom is the answer until you find out, but if you have a particular kind of vision, the best option would be to buy some fast-light primes that fit the way you shoot. You could get all three of the excellent 50mm f1.4 AF, the 35mm f2 AF and the 24mm f2.8 AF primes for less than $1,000 total, new.
The biggest problem I see with the 17-55 is that it's a DX lens. When the D200's time is up, and if you remain interested in street photography, chances are you'll want to go to an FX for the ISO advantage (which I'd say could be as much as three stops going from the D200 to the D3.) You can use the FX lenses on the DX bodies, but not the other way around.
JC