If you're craving some mental stimulation, spend an afternoon at Ignazio Cerio Museum. Whether it's history, culture or beliefs, you'll find lots of interesting displays to keep your mind active here.
You'll have no end of sightseeing choices when visiting Capri. Ignazio Cerio Museum is an ideal place to kick off here, but there are many other worthy places to visit. Marina Grande, Blue Grotto, and Piazzetta di Capri are close to the collection of historical artifacts and will fill in your day nicely.