Too much to do and see but if you get organized, there are a thousand places to enjoy walking and look for what you would like to photograph. I don;t know what you are looking for so it's difficult to give suggestions but I will try.
I particularily like all the Chelsea area and the meatpacking district which is 14th street (fabulous cobblestone streets and even though some superstores have ruined part of the area, there are a lot of fab shots to be found) Great lunch at PASTIS around the corner from Meatpacking...or many other great eating places... you have the Intrepid with the last Concorde on it if you are so inclined... the best part of Chelsea besides the architecture are the funky people walking around. Times Square and the theatre area has its own appeal. I love, absolutely love the architecture on Broadway from about 72nd Street up through and after Columbia University (my alma mater). Riverside Drive and the beautiful old apartment buildings.. great great graffiti uptown if you dare to venture around upper Broadway near the Sloan Kettering Hospital. Harlem, a great place to explore and photograph.
Bookstore: I particularily enjoy three. Barnes and Noble on 6th Avenue (Avenue of the Americas) and 21st street- near the photographers area of town so it is full, full of books on photography and art. Also the one near the Lincoln Center and the one on Union Square (park and 17th).
B and H. Most definitely. remember they close early on Fridays and are closed Saturdays but reopen on Sunday, all day. A lot of temptations.
Downtown, besides missing the WTC, you can still get good shots in Soho, Chinatown, Canal Street, and walk from Chinatown to the South Street Seaport where you can get some nice shots at sunset of the skyline. Also the World Financial Center area (across from the WTC) has its own seaport and sometimes you get Malcolm Forbes' yacht or the Sultan of Brunei or whatever. I really don't know what you like to photograph.
Even better....If you have a car or decide to venture a tiny bit, not too much, you can do it, cross the Brooklyn Bridge, foot, car, whatever, and go down to the River Cafe which is let's say across the East River from the South Street Seaport just a little south from the Brooklyn Bridge----- It's a great restaurant but I wasn't thinking about you eating there necessarily, the terrace in front of it or area adjacent to it is fantastic for sunset shots of the skyline. I was there one night, no camera of course, and these huge tugboats and tankers were coming out of the fog and then you couldn't see the skyline, and then sudddenly you saw this apparition. Quite amazing!
Brooklyn itself has a endless list of possibilities; Botanical garden, Flatbush area, Park Slope, Coney Island. Every place has its "cachet", special flair. Too much and you need a lot of time
Well, if you need anything else, let me know. Too much to do and you will not regret one moment. If you need some nice restaurants or bakeries let me know. I like to cook so I'm picky where I go for food.