Well, as Kuressaare (still) is more a village than a town, the number of cafes, restaurants and pubs is not big. All SPAs have their own restaurants and cafes, but there are certainly several cozy places in the centre.
In summertime most of them have open air terraces, where one can just sit, relax, have a drink or dinner and watch people walking by.
Although you'll be able to find several bars and clubs in the towns (especially in Kuressaare) on this island, my suggestion would be - build a nice little fire (using your common sense and following safety rules), barbeque some saussages, sit around the fire (preferably with people you care about), sing songs, talk, listen to the waves and look at the stars and the moon. This is the absolute number one activity you can do in a quiet and peaceful place like this.