A beautiful, easy going place, Calvi is a dream destination for those who love Corsica: sea, mountains and a citadel all in one go.
My suggestion
I suggest you hire a bike, so that you can explore its nooks and crannies without having to worry about where to park. You can also spend time lazing on one of the many beaches that line the coast.
The GR20 is a difficult trek that is known to walkers from all over the world. It crosses Corsica, from north to south, or the opposite, in 15 days of intensive walking. But seeing the sunset over the Aiguilles de Bavella, or the sheep on the mountain ridges, not to mention the unforgettable views of the sea - aren't these natural wonders worth the effort?