I don't know if it's the cheapest, but we've chosen Ft. Lauderdale for quick getaways because it's a two-hour flight from National and we can always find fares for under $200 R/T. It's also a 15-20 minute cab ride from the airport to the beach, depending on traffic, where everything you need is walking distance or a cheap bus ride away. The beach is so long and wide that I don't think I've ever seen it overcrowded. If the beach is not necessarily your thing, you could check out Taylor Birch State Park for kayaking, biking, hiking and other activities for which they provide equipment.
https://www.floridastateparks.org/park/Hugh-Taylor-Birch