The closest airport is Long Island MacArthur Airport (airport designator ISP) at Islip NY which is about 16 miles & 25 minutes from Stony Brook. This is a regional airport served by major carriers such as American, Continental, Delta, Southwest, and US Airways. Southwest has direct flights from/to BWI and Chicago Midway.
It is also possible to fly into LaGuardia (airport designator LGA) or JFK (airport designator JFK) or Newark NJ (airport designator EWR) but the travel from Stony Brook to these airports is typically lengthy (a minimum of 1.5 hours for JFK & LGA and 2.5 hours for EWR ) because of heavy metropolitan area traffic. More info about NY area metropolitan airports is available at the Port Authority Web Site
Directions and information about how to get to Stony Brook by Rail, Ferry, and Car are available at the Stony Brook Directions Web Site
The Astronomy group is on the top floor of the Earth & Space Science Building. You can find this building in grid C-5 on the online campus map. Proceed to the 4th floor (marked PH for PentHouse) on the elevator buttons.