Definitely rent a car in Saaremaa to explore the island. It's cheap and it's worth it. The buses on the island are slow and unreliable, and you'll be able to see so much more with your own transportation.

A great time to visit Kuressaare is in the mid to late spring. The weather will be warming up, but there will be almost no tourists. It'll still be to cold to enjoy the beach, but the town itself will be opening back up after a long winter. You can explore the island and have it essentially to yourself. Most of the restaurants will be open by that point, but there will be no crowds. The market will have many things again as well.

Before peak season you can also get great deals on rooms and apartments. Head to the tourist information center where they'll set you up with a place to stay. You can negotiate the price down dramatically and will likely have the place to yourself. You can even get a room in a house with a kitchen and sauna for an incredibly low price, so remember to negotiate.