If you haven't already, borrow a bike for a few weeks and see if riding around NYC is comfortable to you. If you're lucky maybe you can borrow enough different types of bikes to see what feels comfortable too. Then go to a shop knowing what kind of bike you want and look at the different options.

For commuting racks are a must. Fenders are only necessary if you plan to ride in the rain. Of course you can't plan the weather, but you'll know which days to leave the bike home.

Single speed is NOT what you are looking for, you are looking for internal gear hubs. They may look the same as there is no derailleur, but they are totally different. You don't want to try converting one as it is more trouble than its worth and will probably cost more than the bike. Since you are buying new, just buy the bike you want with the features you want.

Try Sids on 34th, Toga on the UWS, NYC Velo on 2nd, Bike Brooklyn, R&A, Roys Sheepshead (way down there in Brooklyn). Lots of others, but those come to mind.