Capri mid morning, and walk the town the late afternoon we tried to book a boat for the Blue Grotto and we were to late.
Two days later we came over just to go see the Blue Grotto and the tide was too high for access, we then rented a boat and motored up the coast and that was great fun and sight seeing.

Now back to your question I think one could see the Island and visit the Blue Grotto in one day, if you plan on see the Blue Grotto plan that visit around the tides.