Santorini is a great island but due to the volcano the beaches don't have sand, but smashed rocks (if you understand what I mean). Walk at the caldera in Fyra, Emerovigli, Oia, Fyrostefani and Megalohori. Swim at Kamari, Perivolos, Perissa, Kouloubos, Amoudi and the red beach. Go to a winery and do the wine tasting. Wines in Santorini are tasting very good. I recommend it!
And of course you have to go to the volcano with a pair of old shoes, that you don't need any more, but go during the sunset.
Eat fava, which is a famous food in Santorini (personally I don't like it, but I don't count. Everybody says it's really good) and tomatokeftedes.
At Akrotiri go to the tavern "Delfinia" for fish, and to another one there (I don't remember the name) close to Faros. A very good one is the tavern "Pyrgos" at Pyrgos village and at Fyra "Nikolas" tavern, "Kalderimi", "Selini" and "Archipelagos" restaurant. At Monolithos beach tavern "Galini".
For night life Fyra is the best place to stay. Many bars and great view.
Have a nice vacation.