Much like H&M, Forever 21 has cheap clothes that are great for nights out. Clothing is cheap for a reason (won't last forever), but they're great for the in-style clothes that you won't wear past next season. Small warning: sizes run small
Even though it's a chain, Shakespeare and Company stores are still small, intimate, and filled with book-lovers. Store has wide selection for one so small, and the staff can find any more for you, and order it if they don't have it. Great place overall.
It's far enough north on Manhattan to qualify for a day trip, but The Cloisters is absolutely worth the effort involved in getting there. The museum houses Medieval Art, and has several chapels that have been sent over, brick by brick, from Europe. Fort Tryon Park, surrounding it, is equally beautiful
No need to get the high-end gyms, NYSC is a mid-level gym that has great classes, great gyms, and a wide selection. Trainers are helpful but not overly-so, and they are always good with giving out the free 2-week passes, just in case you want to try it out
Huge variety of clothing, from designer stuff to $5 t-shirts. Great 'cool' clothes at affordable prices. Their vintage section is particularly awesome, and definitely worth a look
It's almost always crowded, and the lines for dressing rooms can be a nightmare, but H&M is totally worth the trip for cheap clothing. Decent selection. The staff probably won't help you out much, but they at least look like they're having a good time hanging out there.
The staff aren't particularly knowledgeable about wine or liquors, but they know every bottle in their store and can find it for you. The selection is enormous, and everything is very cheap. Strange that it's in the midst of NYU territory.....
Astor Wines always has weekend tastings of some kind of themed wine - Wines from Greece, or New Pinot Noirs, that sort of thing. Selection is good, though runs a bit more higher end than most liquor stores. Good selections of wine racks, as well
New York has an incredibly rich and interesting history. Unfortunately, the Museum dedicated to it only shows bits and pieces of it. They have very few permanent exhibits, opting only for temporary exhibits on certain people or era. Sometimes they're interesting, other times they're not. The New York Historical Society is a much better place to get some true New York artifacts and to see the entire history, not just parts of it.
While the building itself is extremely cool, the Guggenheim actually holds very little in the way of artwork. Occasionally they have older exhibits, but most of the time they are ultra-chic post-modernist art that is somewhat unintelligible to those not a fan of it. Fairly pricey as well, if you're in town for only a few days, I'd hit up other museums before this one.