As a pilot I have had the chance to fly to many small airports in private airplanes, and Catalina is one of them. This airport sits atop the edge of a cliff at one of the highest points on the island, flanked by cliffs on either side and a dirt strip used to land an old DC-3 flying cargo in from Long Beach (quite a sight, though I think they don't do that run anymore?).
The airport itself is quite challenging, and I have trained many pilots on the landing techniques used there. Certainly, not a place a private pilot should try without an instructor or the mentoring of a friend who has been there before. The runway is rough, with many bumps, potholes, and optical illusions. Despite this it is a fantastic place to fly.
During the summer they have bbq cook out nights right at the airport restaurant, with live music and delicious food. Even on a regular day, you can fly in, grab a buffalo burger and enjoy the serenity that is only a 30 minute flight south of the busy Los Angeles basin.
If you're staying in town, it's a fun place to visit for the unique atmosphere, some outdoor plaques and exhibits talking about the island, the yummy cafe, and the gift shop. With no fences, TSA, or any of the pains of a typical airport, this place really embodies what flying used to be to the general public, so grab a burger, sit at the edge of the runway and watch the planes touch the edge of the clouds that sit just at the end of the field.