I was in Santorini a couple of years ago, and some things I can recommend are:
1) Walking around Oia and watching the Sunset (and the
postcard views). We stayed in Oia for the trip.
2) Taking a sail boat tour of the caldera (ex .
http://www.vacation.gr/tours/santorini/cal...ia-sunset7.html ) The boats leave from lower Oia and you get to swin in the hot springs and visit both islands in the caldera.
3) Wine cellar tours and tasting (ex.
http://www.boutari.gr/ )There was one a few kms from Oia.
4) Dinner at the bottom of the cliff in Oia
5) Rent a motorcycle and drive aimlessly around the island
6) Stay away from the Fira, its a dump.
7) The beaches (red and black sand) in the south are supposed to be good, but we stayed more towards the north.
8) Cliff diving near lower Oia
9) The retsina, grilled octopus and ouzo are always good...MMmmm