Santorini

All of the island. People rent ATVs to get around the island.
It is not especially a big place. But it is beautiful.

Fira has the most nightlife but the 2 main beach resorts, Kamari and Perissa, have lots of bars and cafes as well, and water sports activities during the day.

We are staying in a fabulous place with a caldera view in Akrotiri. We only have one full day there. I am wondering if it is worth it to take a five hour sailing trip that goes up to near Oia and to beaches and the hot spring, or just stay put.

Fira probably, we are older and stayed in Oia and other than the cruise ships it was great. Kamari was fun as well and a lot quieter than Fira which gets pretty crazy. Enjoy!

dianamerrifield, the hotsprings is a sulphur-smelling cove of lukewarm and murky sea water that you have to swim 50 meters to reach from the excursion boat. The murky water in that cove will permanently stain your clothing. Relax and enjoy what Akrotiri has to offer and be sure to go to the archaeological site there. Do it when they first open in the morning at 8 am before the busloads of cruise shippers start arriving. It's magical then.

Fira for sure

There are four towns - Fira, Oia, Imerovigli, and Firostafani - located on the Santorini cliff.
Where will you be staying? The most vivid part of the island is Fira. All four towns are a great place to stay if you are looking for a view to the caldera. Your night out in Fira town will be amazing since there are plenty of choices!!

Some suggestions:
Clubs to check in Fira: Enigma, Koo, Town Club
Go to the stylish Tango bar for cocktails
You can find a more laid back crowd and music at the Tropical
Watch the sunset from the fairy tale Oia
Check out Vlychada beach, you can find there a quite famous tavern named "Psaraki"
If you like eating fish you can go to Ammoudi Bay "Katina" or "Dimitris" are the favorite spots for locals
You could try Parasailing while watching the sunset
Go on a boar trip to see and hike the Volcano, plus swim in the hot springs :)
There is also a Jet Ski Tour to the Volcano
Go Sea Kayaking
A night at an Open Air Cinema in Kamari is a must!
Go Greek Island Hopping - Santorini can be combined with other islands like Paros, Naxos, Ios, Mykonos, Amorgos, Milos & Folegandros