If you're going to do the Empire State Building, get there for opening time (think it's at 9 - we aimed for about 8:45). Much more manageable queues then. And be prepared for the fact that getting to what you think is the front of the line (i.e. the entrance) is absolutely not. There are queues for security, queues for the first lift, then for the second (walk the stairs for that one. It's only a few floors!)
We attempted to visit Ground Zero, but think we got the wrong side of it, as it was just hoardings shielding the building site. However, it was worthwhile going to the church there, where the firefighters took restbreaks. There's a display in memory of it all and is very interesting.
The hop-on, hop-off tour buses are worthwhile to get your bearings initially.
Also, the queue for the Liberty Island boat tour was about 2 miles (or 2 hours) long! If you want to stop off and climb up (which wasn't an option 18 months ago) you don't have much choice, but we were only looking at it from a distance, so hopped on the Staten Island ferry instead, with no wait, and as good a view.
There are evening (and daytime) cruises on the Hudson which are good. We did one that left in daylight, so we saw the city then, but came back at night, so we also saw it lit up. Plus Statue at night. Awesome.
Horse and carriage rides round Central Park are an absolute rip-off. They'll quote you a price for half an hour, but which is only 20 minutes, and tell you that the tip is on top of that. And get arsey if you mention that surely that's optional.
We did the subway. Once. Nightmare. I have a good sense of direction and can usually find my way round anywhere, particularly in London, but the mapping system there was the most confusing I've ever seen. And you need loads of change. You can pay by credit card in a machine but it wouldn't accept mine as I couldn't off a zip code for residency! Dunno what I was doing wrong, but after that we took cabs everywhere. Actually turned out cheaper for 4 of us. Oh, and make sure you do use the yellow ones. We avoided a major rip-off by someone touting for business after the evening cruise who quoted $35 for a trip which was about $7 in a yellow one.
Had problems finding public loos. Kept having to go to cafes - where inevitably there was only one (grubby) one and a queue.
I love America, been there loads of times, and NYC is without doubt the dirtiest, graffiti-daubed, aggressive city I've been to. But undeniably exciting. Glad I've experienced it. Not sure I'd go again, however.