Most of the shops in Visby are located in the area around the street Adelsgatan close to the ringwall. There are also many shops in Östercentrum close to the gate Österport including some bookshops, department stores and supermarkets.
Since Gotland is full of sheep, this is the obvious souvenir with things like slippers, vests, hats, gloves and things for your home and your car. Most of it in the dark grey colour of the local sheep. You can buy things all over the island, both at Visby souvenir shops and local farms you pass in the countryside. Look out for "fårskinn" on signs.
Prices vary enormously depending on what and where you buy it but it is generally a more exclusive souvenir.