The touristy New York weekend goes: Times Square, Central Park, a Broadway show, Empire State Building, a diner, dinner in the West Village. It is a fine weekend. It is also almost identical to what six thousand other people are doing at the same time as you. Here is one that stays across the East River and lets you meet a different city.
Stay in Cobble Hill or Long Island City — both are 15 minutes from Manhattan by subway or a good walk over a bridge. Cobble Hill is where locals under 40 actually live and eat. LIC is quieter, has better waterfront views of the Manhattan skyline than any Manhattan viewpoint, and no tourists. Skip the Strand queue and go to Books Are Magic on Smith Street instead — smaller, weirder, actually a working bookshop with old furniture and a reading nook.
Eat at Frankies 457 on Court Street if you can get a table, or Rucola nearby if you cannot. Both are Brooklyn restaurants that a local would take an out-of-town guest to, not a tourist trap. Do coffee at Devoción in Williamsburg — they roast Colombian beans in the shop, big space, no rush. And on Sunday morning walk the Red Hook waterfront, which has views of the Statue of Liberty most tourists never see because it is inconvenient to reach.