[Mike80911]

As for a shooting range I only know of one in the city. It is on the westside and I think you can only shoot a .22 rifle there without a permit so kind of a waste of money.
As for a real burger joint go to the Burger Joint at the Parker Meridian hotel 57th Street between 6th and 7th Avenue it is behind a black curtain just past the front desk.
There are a lot of small museums around like the NYC History museum, the NYPD museum, the subway museum and the tenement museum. South Street Seaport is fun to visit and near ground zero and some of the small museums I mentioned.
As for car gatherings nothing in the city itself most of them are in Long Island or Westchester and if you don't have a car not easy to get to.
Stay out of the Times Square area or Midtown when it comes to eating all of those places are tourist traps and the food is terrible. Go uptown past 57th street the further up the better. Many places on upper Broadway like Carmines on 90th street and Broadway or downtown in Chelsea or the village to eat.
You can spend a day on the tour busses there are some that you can get off and on as you please with a day pass.
Have fun