The best price found from United States to Slovakia is on October 28th, 2015, travelling with Austrian Airlines. See more options, compare prices and book: search flights.
Bratislava's intra-European airport, 9km northeast of the city centre, is small. Unless you're coming from the UK, which has several direct flights, your arrival is likely to be by train. Vienna in Austria has the nearest international air hub.
The main airlines operating in Slovakia: