If you're all fancy-like, there's also the option of taking a helicopter from Island Express Helicopters, which's totally rad and only takes 15 minutes, but is obviously a teeny-tiny bit more expensive, and drops you off far enough from town that you're going to have to take a cab into Avalon... which adds another $20 or so to the trip.
Once you're there, you're on foot the whole time. That is, unless you want to rent 1) a bike, or 2) a golf cart, which are both available at a zillion rental stalls that charge by the hour, and capable of taking you up to scenic views and cool, off-the-wall places (see: hidden pet cemetery) that're an easy ride, but a tough hike. Neither, though, are necessary to get around. Oh, and if you're staying overnight, there're a number of hotel options (our pick: the Pavilion Hotel, which was recently remodeled and is right on the beach), as well as rentable houses.