I reached Visby in 3 hours by ferry from Oskarshamn, a short train + bus journey from Kalmar.
After entering the town through the Osterport, I spent a morning walking the streets of the old town visiting the various ruined 12th century churches, as well as the more interesting and undamaged Domkyrkan.
I found it a shame that Visby's waterfront was obscured by huge storage tanks.