Having just returned from a grat eight days in NYC, these are a few of the thoughts that come to mind:
Take the best walking shoes you can afford and walk as much as you can. It is the very best way to see/esperience/feel the city.
Take clothes for heat if you go in the next several months....the humidity makes it seem even hotter than it is
Divide your days into neighborhoods and identify what you want to see/do in each. All are very different...Soho very trendy; Chelsea, artsy, fun to visit Chelsea Market; Greenwich, charming and fun; midtown, busy and professional; Time Square completely insane; Upper West Side, full of life, Upper East Side...very classy, clean, and reeks of old $$$.
Allow plenty of time to spend in Greenwish Village and consider taking the Food Tour which is also full of historical information and interesting comments on village life. Also includes a visit to Chumley's, something I would never have found on my own.
Ride to Brooklyn, walk on the Promenade and walk back over the bridge...the views are incredible.
The Harbor Lights Cruise is a different perspective and really neat when the lights of the city come on.
You don't have to spend a fortuyne on food....but do allow a splurge or two.
Take lots of photos so you will remember everything.
Use the subway. I never felt uncomfortable, people were very helpful when needed for direction, and the musicians and dancers are amazing, especilly around the 42nd street station. It can be confusing but I was doing fine after the third day, well, most of the time!