There was a tiny bit of construction being started last time I went to ground zero about 9 months ago, so I'm sure there's been a little progress made since then. Either way, it's worth going to see.
Don't eat in Times Square unless you want to get your wallet raped. Some good BBQ can be found at this place called Dallas BBQ. They have a few locations (one in Times Square actually) and if you go for the early bird special, you can get some pretty cheap ass BBQ that tastes great. Another option is Brother Jimmy's BBQ. I think there are a few around town but the one I know of is on 31st and 8th by Penn Station.
I second all the recommendations to check out SoHo and Chinatown. There's a lot of really cool things to see and do, mostly in the form of weird and niche shops. Check out St. Marks place in the East Village for a lot of that stuff as well.
An oft-overlooked recommendation... If you need to use the bathroom, go into any Starbucks. They don't care if people use their toilets.
Another thing to do - Walk the Brooklyn Bridge. It's beautiful and a brisk walk. When you get to the other side in Brooklyn, you'll end up in the neighborhood called Brooklyn Heights. Right around the corner on Old Fulton St is
Grimaldi's Pizza. If you haven't heard of it, it's the supposed best pizza in NYC. Having tried it, I must say it is pretty fucking fantastic, but know that there's always a line way out the door unless you get there around 10:30-11:00 AM before it opens. Also, you can only buy pizza by the pie. They don't do slices. Either way, it's worth it.
Jam it back in, in the dark.