As a NYC resident, NYU is in the heart of the village and has no "campus". Buildings are scattered about and some bldgs. clustered together... In the middle of the day and rush hour, the streets are mobbed, shoulder to shoulder of students, commuters and other city residents. Exciting to some, claustophobic to others. There is lots of energy and some love that NYC energy. Just be aware, that it will also take some energy on your part to connect to other students, since, you may not bump into people you know from class to class. NYC is a big city with lots of cultural offerings, but it is a city in the truest sense.
Just came back from RPI yesterday, and it is a totally different animal. RPI has a campus with lots of green and the typical grassy quads, recognized engineering program and a very good chance of job offerings at grad., but the facilities could be better maintained (paint peeling windows, bird nests on ledges, graffiti). Engineering buildings have a very industrial, cold feel (cinderblock walls, cement floors)., but they are well equipped with all the "equipment". Dining hall is okay, not like NYC with all the food choices - restaurants in the area, but beware, that would be more expensive too. RPi is secluded, with the Troy the city down the hill, depressing and dismal, with lots of hobos. NYC has bums, too, but with the crowds, they're less noticable. So, I think it's a hard choice, RPI better engineering school, NYU city lifestyle, more culture, entertainment options. Also, don't forget at RPi, you are surrounded by engineer types, NYU, all types. (so much so, that you won't know who goes to NYU or who is just passing by). Good luck! let me know if you have any more questions.