The real question is, are you planning on doing any touristing.

If you are, get a CityPass. It costs in the region of $100 and gets you into five tourist attractions that would cost over $200 if you paid separately (or some such equivalent sums). I think it includes the Museum of Modern Art, the Natural History Museum, a Circle Line boat tour, the Empire State Building, aaand... something else. The Guggenheim! Even if only do three of these things, you're saving money.
http://www.citypass.com/city/ny.html - ooh, it's either changed a bit, or my memory is fuzzier than I remembered. It now includes the Metropolitan Museum of Art and the Cloisters, which is nice, and is $74, with a saving of almost $74. XD
If you want a sky-high view of New York but fear the giant queues or just fancy something a bit different to the Empire State Building, do Top of the Rock at the Rockefeller Centre. You're not as high as at the Empire State Building, but when you're up that high it doesn't make much difference, and your sky high view of New York will actually include the Empire State Building, which makes a nice change. :3
If you're not planning on checking the internet more than briefly, dare to be cheeky: don't spend money on an internet cafe, and instead head for the Apple store on 5th Avenue. It's open all hours, should you get to 2am and decide you need to buy an iPod, and they have computers that are internet-ready and open for play.
I stayed at the Portland Square Hotel last time I went. Cheap, very basic, and BRILLIANTLY positioned. If I hadn't already decided to save money by going for hostels next time (if you're really not fussed about sharing a room with strangers and want to save beaucoup cash, look into Jazz Hostels. If you'd rather be more central and not necessarily save *that* much cash, the Big Apple Hostel), I'd stay there again for the location alone.