For crowding, I would avoid the US Thanksgiving weekend (November 23 through 28 in 2011) but otherwise, so many millions live and work in NYC that it’s pretty hard to tell if it’s crowded or not. However, certain events in town can REALLY drive up hotel prices, so it might be best to pick your time based on when you can find a decently priced hotel room. Shop around a lot. One hotel may have an on-site event and very high prices while the one next door has some “low” cost special rates. If you’re driving be sure to figure parking rates into the hotel calculation. Parking may be $40 a night, so “parking included” is a big deal.

As for weather, I would try for late spring or early fall. Late September/early October is ideal for weather although the “fall colors” in New England (usually best starting around Oct 5) might mean there will be more tourists around. Summer is also fine, although there will be more tourists. Winter is “no problem” although I don’t think it’s a great time to be a tourist as you’ll be spending a fair amount of time outdoors.

For the most part, NYC never closes…. Like anywhere, lots of things close on Christmas day, but that’s about it. July 4 brings lots of special events and most shops and perhaps a few attractions will be closed. Whether or not you want to avoid it due to increased prices, bigger crowds, a day when you can’t shop or embrace all the special activities is a decision for you. Same with Thanksgiving weekend with the big parades. I would check the websites for the attractions you intend to visit to see the holidays that a specific place will be closed.

New York will be no more crowded than Paris, London, or Barcelona. It’s a dense, walkable city, and “crowded” is part of the territory. But it’s not overcrowded, so don’t think you’ll get swept up by a mob, or expect to see people riding the on the roofs of buses and trains, or anything like that.

I agree with oldlady: Mid-to-late spring and early-to-middle fall are probably the best times for NYC, and I’ve always felt that October is a very good time to visit the United States, as the weather is pleasant everywhere in the country for most of the month, and you also get to experience Halloween. Even if you don’t stick around until the day of Halloween itself (31st of October – by which time it’s usually quite cold), just the buildup to Halloween throughout October can be a very rewarding cultural experience while visiting the US. Do make an effort to take a side-trip to Boston.

Personally, I’m not a big fan of November-March in New York City or anywhere in the northern United States; the weather is cold and absolutely miserable. Avoid Thanksgiving and Christmas like the plague (Thanksgiving is best experienced in a home with traditional Thanksgiving cooking, not out-and-about in the miserable cold).

On the other hand, the city empties out during the summer bank holidays (Memorial Day weekend in late May, around Independence Day 4th of July, and Labor Day weekend early September). However, the touristy things (Empire State Building, Rockefeller Center) will probably be more crowded those days with out-of-town visitors. All weekends in general the city is less crowded.

Summer inside Manhattan and much of Brooklyn can get pretty hot, as New York is one of the cities that experiences the heat island effect, in addition to the fact that the entire eastern half of the USA can be humid as hell (although, northern cities like New York, Boston, or Chicago may have variable summer days, hot and humid one day, cooler/drier and more pleasant the next).

Have fun!

Best time is really the summer. Lots of funfare and walking. Cruise and boat rides both in NJ and NY.
Similar to London. Cheap accomodation can only be found at hostels or a little away from NYC, such as the suburbs.
I live right across the river in NJ so feel free to ask any further questions.