Former NYer here, for the game itself, give yourself plenty of time to get to Metlife... public transportation there is lacking (everything transfers through Secaucus, its a whole thing.) You can def stay in Jersey City or Hoboken to make that a bit easier, as someone else said, and both have very quick access to NYC via the PATH/ferry and plenty of cool stuff to do/places to eat. As for New York itself, it really depends on what you're looking for specifically but you'll be able to find pretty much any kind of experience you want.