In 2 or 3 days
Fira is worth checking out as the views and the town itself is pretty stunning but it is expensive so after arriving in Santorini, take a local bus to Fira – have a look around and then move on! Stay in one of the beach resorts like Perissa – spend a day swimming & snorkelling and soaking up the sun, eat at the local tavernas on the front – most of whom do a set menu and a karaf of wine for a reasonable price then get a good nights rest. Visit one of the ruins, if you are staying in Perissa Ancient Thira is close by – you can even walk it in a hour but it is steep and take plenty of water. If Akrotiri is your choice take one of the local buses to Fira, get off at the intersection where the road and the caldera meet and catch the bus from there to Akrotiri. You can walk it but it takes a while. After the culture and activity of your second day, take a boat trip out to the volcano and caldera, lunch on your boat and swim in the hot springs…
In 7 days
With a week you can take things at a much more leisurely pace – take a day trip to Fira and take another day trip later in the week to Oia, pack a lunch or buy a gyro off the beaten track – eating and drinking in both towns is expensive – remember to hang around for the sunset. Visit one of the splendid wineries and sample some of the local wine it’s surprisingly good.
In 2+ weeks
With so much time it’s worth getting a ferry to one of the other islands in the Cyclades – Mykonos is 3 hours away by catamaran and is a lively island. Ios is around an hour away by high speed ferry. Check local websites for the schedules and prices.