Visby is a fantastic small city which throws you back to the medieval time, especially if you go there during the medieval festival time, which use to be the first whole week in August every year. During week 29 in July Visby is invaded by Stockholmers youngsters and the partying nights are wild. Many Visby locals escape from there during this week.
Except from the old ruins, cathedrals and other architecture attractions, there are also wonderfully picturesque small houses at cobblestones streets, a town market, concerts just to mention a few attractions.
There are also many great things to discover nearby Visby, so I highly recommend a tour around the whole island of Gotland as well.