My husband and I recently returned from a 4 night stay in Capri, so my vote would be to stay overnight. The center (Piazza Umberto) of Capri has a different feel once the sun goes down, the day trippers leave, and the locals come out in their chic attire to go clubbing and stroll the town center. During the day, you could first go to Ana Capri, stroll unhurriedly through the lovely town and small shops over to St Michael's Church to see the tiled floor, take the chairlift up Monte Solaro to see the amazing views, and tour Villa San Michele with its pleasant gardens and gorgeous views of the harbor. Have a leisurely dinner, wake up early the next day for a boat tour around the island and to see the Blue Grotto before it gets too hot and too crowded. If you just go for a few hours on one day to Capri, I think you would get a totally different feel for this breathtaking island.