I'd go back to Metro Bicycles (http://www.metrobicycles.com/) if I needed another bike in NYC. I bought a Dahon Speed D7 (http://us.dahon.com/bikes/1728/speed-d7) folding bike from them a few years ago. Its cheap ($500 so I didn't worry about it getting stolen), adjustable (so I could easily change riding positions as necessary/sore) and fit easily in the apartment I was living in at the time.
As for accessories get this: http://www.strava.com/ for geeking out and a U-lock with cable like this: http://www.amazon.com/Avenir-Standard-U-Lock-Cable-Lock/dp/B... for security. The cable makes the u-lock more useful and most lock companies will insure the bike theft if you are using their lock when its stolen up to a certion $ amount.
Don't worry about flats etc because there are enough shops around to fix them within an easy walking distance. All the gear you strap to the bike is just something you'll have to replace once it gets stolen (either the bike or just the stuff on it) or falls off while cruising through town.
Also JWZ has some solid recommendations here:
http://www.jwz.org/blog/2008/05/the-collected-jwz-bicycle-wi...