I've never been to Santorini, but for CFU my suggestions would include:

- Visit the Achillion ruins
- Visit the Kanoni area and watch the airport activity (I'm not really a plane spotter, but it's great to see aircraft take off and landing from above!)
- Visit the impossibly small streets of the old town ("Kantounia")
- Go up the seaside Fortress.
and make sure to eat some of the local specialities (preferably in one of the taverns in the aforementioned small streets of the old town), like Sofrito (veal-based), Burdeto (fish-based) or pastitsada (like a mild chicken curry with pasta!).