I'm gonna check out what "cyclocrossable" off-roading there is over the GWB eventually. As for climbing walls, the one near Lincoln Center sucks; poor route setting, questionable safety, and hands down the dirtiest gym ever (it doubles as a makeshift homeless shelter). PM me if you want to find out about good climbing walls in the area.

And to answer FraAngelico, Riverside Park is questionable as far as deviating from the paved bike paths. I've heard that cyclocrossers train there, usually in the mornings. Generally, you can't speed there as you might get a summons, if you don't first plow into a skater, jogger, powerwalker, or dog. I doubt, though, that it is not as patroled during the late fall and winter when snow and mud take over, the non-bikers dissapear, and urban miscreants like me shod the rims of my CX bike with knobbies. In reality, there aren't too many unpaved paths, just some dirt-paths worn into the grass alongside the paths between 97th street and the low-100s. You can improvise a psuedo-cross course by incorporating the many staircases, though.