Flight
Both JFK Airport and LaGuardia Airport are in Queens and within reasonable distance to the venues. JFK is much larger and is also much closer to the reception venue in Long Island so if you're planning to book accommodation in Long Island, it will be the best bet. Newark Airport is quite far from Queens and Long Island and it'll involve a long commute across Manhattan so we wouldn't recommend choosing Newark :)
Travel Note
We recommend taking up accommodation in western Long Island (east of Queens) as it'll be centrally located and proximal to the wedding venue, reception venue and the airports - specifically the towns of Westbury and Garden City. The Fresh Meadows neighborhood in Queens is also a very good location. We've listed a few of the hotels here - - Fairfield Inn and Suites, Queens/Fresh Meadows - Courtyard by Marriott, Queens/Fresh Meadows - Courtyard by Marriott, Westbury - Hilton Garden Inn, Westbury - Hampton Inn, Garden City - SpringHill Suites by Marriott, Garden City - Hyatt Place, Garden City - Four Points by Sheraton, Plainview
Travel Note
Hiring a rental car at the airport will be the most convenient option. There aren't many subway stations in Central Queens and the frequency of the Long Island Rail Road (LIRR) trains is quite truncated during weekends and outside rush hour so it'll be cumbersome to plan around public transport :)