The short answer is that the bus is the easiest way around the islands. There is also a wonderful ferry system, yet that runs less frequently, but we still found it very convenient. Here are links to the ferry
routes. For the bus routes, use the map for the "Western areas." Verify the ferry times when you get there, in case they change in October.
As for best places to visit -- that depends upon your interests. Are you looking for beaches, history, architecture, nature/zoos, or something else? If it's a little bit of all of the above, what is the most important?