The closest airport to Galveston is Houston Hobby International (HOU) and a 40-50 minute drive depending on traffic. There's a second airport in Houston as well, George Bush Intercontinental Airport (IAH), but it is a little further north and closer to a 75 minute drive to Galveston. If you don't mind the extra drive and plane tickets are better into George Bush International, you can definitely fly into that one.