You said, "Go anywhere," which to me implies dirt trails may occasionally be ridden, and so you might want to run fat/knobby tires occasionally, thus requiring cantilever or V brakes. That to me would mean: Singlespeed cyclocross bikes...
Bianchi San Jose (being blown out at my LBS for $450)
Motobecane Fantom Cross UNO (mail order only?)
(basically visit your LBS(s) and ask if they carry any SSXC bikes.)
...But then you said NYC riding, which doesn't have a lot of dirt outside Central Park, right? (Forgive my ignorance, I have only been there twice, and did not see much dirt in Manhattan). In that case you're just talking about "go on any street" and your options open back up to pretty much anything that catches your fancy.
Help me understand what you mean by "Go anywhere".