Except for down in the very small city of Avalon near the beach, Avalon is pretty hilly. I even find it difficult to hike. There are some bike rides going toward the east end (to the left of the city when the ocean is at your back) and some going past the old casino around to where the newer condominiums are located (to your right with the ocean at your back). There is a road that goes to the small airport, but you have to get up to it. It all depends upon how seriously fit you are. I am not a biker and there are so many water related things to do at Catalina and I just would not plan on focusing my time on biking, but if that is your passion, you can find the biking. Just realize Catalina is pretty mountainous. There is a road that goes to Little Harbor, to the airport, and a road to the Isthmus which is quite a long bike ride but doable in a day, maybe even round-trip, although I am not sure (still not a cyclist).
