In Gozo, there's no point in visiting villages unless you like churches and even when you're not usually that much of a fan, there are still some that are worth seeing!
Archaeological sites are also very important.
Unsual and spectacular
Free entrance
Basilica
Ta' Pinu at Gharb
Exceptional archaelogical site & museum
Ticket for the mill of Xaghra + Ggantija 7€
Ggantija
A panorama of the whole island
Free entrance
Gozos Citadel
The most beautiful and interesting museum
Thecathedral
The craftvillage (I didn't like it too much but it depends on taste)
Craft Village
Grand and beautiful panorama
Ascent in the Rotunda 3€
Xewkija Rotunda
Victoria Park, very cute and decorated according to the seasons
Villa Rundle
Many vestiges, dolmen, stone circles are visible during a walk