Well that depends on your budget and desired location - how close you want to be to certain attractions, what you want from an area, etc - think of NY as a collection of small villages lumped together, each with their own atmosphere and vibe. Most areas in the city are easily accessible, taxis are cheap and plentiful and the subway is efficient (though the map takes a little while to get used to as it's not as explanatory as London's). My advice would be to avoid anywhere budget, purely as you won't know what you're getting and facilities are usually shared. We usually stay at the Affinia Manhattan on 7th Ave because, as far as we're concerned, the location is perfect - over the street from Madison Square Garden with Penn Station (the NY equivalent of King's Cross with the 1, 2 and 3 subway lines that run north-south of Manhattan passing through it) underneath it, 10 minute walk south from Times Square) one block from Macy's and about 400 yards from the Empire State Building. A further 15 minute walk south (don't worry, it's all perfectly safe) and you're in the heart of Greenwich Village. There's a fantastic deli next door where we would go every morning to stock up on fresh-made sandwiches, juice, water and fruit for lunch that was dirt cheap.
Other good ones are the New Yorker on 8th Ave and 34th Street and the Wellington, further up 7th Ave about 2 blocks from Central Park - both clean, decent 3 star accommodations. A good site is
http://www.nyc.com which is the official NY tourist website which has details of most of the good hotels in the city.
Don't be adverse to Brooklyn either, which is easily accessible from Manhattan and considerably cheaper. Brooklyn is a great place (it's the equivalent of being 'south of the river' in London) and is probably how most people actually visualise NY in their minds.
any more Q's, let me know.