How about must don'ts?
You should have beautiful weather. Mets are only team in town for the weekend. Where are you staying? That can influence matters significantly. I like the City in measured doses.
I'd never send anybody to Times Square, or the Empire State Building. I just don't think either are worth the hassle/cost/enjoyment. Times Square? It's mildly more interesting than Rockefeller Center and the boobs who stand by the window at 7 am of the Today Show. See the Statue? sure, there are ways to do it, via a Boat tour perhaps if that interests you. I prefer more discrete, less obvious NYC experiences. My lone exception is probably the Met, and if time allows Central Park. (conveniently the Met sits on the East perimeter of the Park). Don't eat at Peter Lugar's unless you want your steak sliced for you like you're seven years old. Katz' (East Houston St.) would be OK, if you really have to do a signature tourist trappy restaurant, if you must have pastrami on rye for $20 or whatever. Hard to give restaurant tips, as reservations may be tough to manage, based on your time/schedule etc.
Most of my trips to NYC are business, so I've got a lot of miles on my feet walking around downtown/financial district. It used to be a ghost town at night and weekends, but I think it is picking up interest. If nothing else, visiting the WTC site. I usually stay at one of the hotels next door to WTC (on Church St on the east) or Albany St. to the south, so I've seen that whole site at every stage since about '04. It is quite a visual, and I still have yet to visit the official Memorial. It's also fun to walk around SoHo and Greenwich Village and visit shops and what not. It's a much more laid back spot in Manhattan relative to Midtown. Further north of the Village is the Highline and Hudson Yards project, which that project is HUGE. I haven't been up there in a couple years, but people love boasting about the Highline.
I still try to hit a spot in Chinatown every visit, which isn't far, (from downtown) and of course has taken over Little Italy (pro tip: there really isn't a Little Italy anymore in NYC, the Italians have long since moved all over the place). Some damn good meals to be had in Chinatown, I only know the places by sight and led in by locals.
As you no doubt know, Brooklyn is where all the cool kids live. It truly is the Wal-Mart of counterculture. It can be fun too, though as with Manhattan, there's a helluva lot of different neighborhoods. I have a limited rolodex of ideas.
Midtown is busy, crowded with tourists, think a busier, more expensive Michigan Ave. (Chicago). East Village is also full of people who are cool for a living (many it turns out are from Ohio). I jest a bit, but the point really is there are a lot of different experiences you can have in NYC on a weekend. Just know that $20 will fly out of your pocket about every 30 minutes or so.
