What should I do if I get to spend 2 nights in Gatwick London, UK?

trying to take a plane to london, then to croatia and back. but the flight times don't match and I get to stay over london between flights. Should i stay in a Gatwick hotel or should I take a taxi directly to center london and stay there? I don't want to drive, and want to make sure I stay in a safe place. It seems to be a 30 mile hike to the center city from Gatwick. Any interesting places I can visit closer to the airport?