I'd pick your hotel based on 2 things:

1) That it has the amenities you want at a price you can afford
2) It has easy access to multiple subway stations

Notice I didn't say "close to XYZ site". The subways will get you wherever you need to go quickly, so stay somewhere that has good subway access. When we went, we stayed in the Holiday Inn in downtown Brooklyn. Definitely not in the heart of well-known tourist attractions. My wife picked that one because it was close to where she needed to be for the conference she was attending. Knowing what I know now - I'd still pick that hotel, but not because it was close to the conference... she still had to take a Subway to get there. I'd pick it because within a few minutes walk from the hotel were subway stations that serviced the A, C, G, 2, 3, 4, 5, B, Q and R subway lines. Between those, we were able to easily get everywhere from Yankee stadium up North, Coney Island down south and everywhere in between. It was really convenient. It was also a nice hotel in a decent enough neighborhood.

So, don't pick your hotel based on the tourist sites you'll be visiting, but on how easy you'll be able to get to/from the tourist areas - because even if you stay right across the street from tourist area A, you'll still need to travel to get to areas B, C, D, etc.