What are the best things to see and do?
Been there a couple of years ago, and from what I recall:
1. The market place and old town around it
2. The city walls
3. The Gotland museum
4. The seaside walk
5. All the church ruins
Visby is a small town, you can do most things in a day. The ice cream shop „glassmagasinet“ near the harbor with their about 100 flavors is another fun thing, and there was a medieval themed restaurant, plus some small craft run restaurants, cafes and ice cream shop around the market.
If you are there for more than a day, consider renting a bike for a trip along the coast, or a bit longer by bus or boat.
Hi there, we loved Visby, truly a medieval gem without crowds, unless the cruise ships are in town. Carlos wrote an excellent trip report on his visit - https://community.ricksteves.com/travel-forum/trip-reports/trip-report-stockholm-gotland-sweden-aug-20
Here is the cruise ship schedule if you want to plan around that:
https://www.cmport.com/terminals/ships-in-port/
Sadly, they don't list the ship size (though you can look that up easily enough).
I spent one night (30 hours) in Visby about 3 years ago and was able to walk every street in the medieval town during that period. I would caution you that Visby has a lot of special events and festivals on summer weekends. Those dramatically affect lodging costs and sharply reduce availability. Unless you have a special interest in one of the events, I'd suggest planning to visit during the week.