There are three airports you can fly into: JFK, La Guardia and Newark. With no traffic, LaGuardia is about a 15 minute cab ride from Williamsburg, JFK is about 35 minutes and Newark is about 45. You can also take public transit. From Newark, take NJ Transit's AirTran to Penn Station, then ACE or 123 subway down the 14th Street where you can transfer to the L into Brooklyn (Bedford Ave is the first stop). From JFK, take the AirTran to the E at Court Square, then the G into Greenpoint. For La Guardia, just take a cab.
Nope! In fact, trying to park in Brooklyn or Manhattan will be a nightmare. The subway can take you just about anywhere you want to go! You can use Google Maps to see the best train lines for your destination. Not interested in taking the subway? Cabs are readily available, and ride sharing apps like Uber and Lyft can get you anywhere you need to go.
If you're not staying at one of the hotels close by, you can grab a cab/Uber/Lyft.