Avalon is a small town and it is easily walkable. If you prefer, you can also rent a bike or a golf cart to explore the island. Golf cart rentals start at $50 for two hours.
If you have extra time, consider taking a scenic helicopter tour of the island or hiking to the top of Mount Ada for stunning panoramic views. If you have less time, skip the walking tour and spend more time enjoying the outdoors.
The closest airport to Avalon is the Catalina Island Airport (AVX) which is located in the city of Avalon itself. It is a small airport with limited flights, but is just a short distance from the center of town.