Up until recently, all the cruise ships would send people to Thera. This the place with the donkeys and the stairs and the gondola. Thera is a tourist trap. Its all the same kitchy shit you see everywhere. Now they have a new port which is even more south, so people take buses to Thera, and takes even more time to get there. If they take a tour of the island, they usually fly through Oia. The other problem is if you stay for the night Oia is packed with everyone trying to get that one Instagram picture. A whole island of tourists all trying to squeeze into one spot, people literally hanging off buildings.
So the way to enjoy it is find a time where it isn't packed and enjoy relaxing. It is not a do something island, it is a good do nothing island. Mykonos has the beaches and the clubs, but they also gets very crowded during tourist season. Everyone wants to be in the town, there are some decent hotels and Airbnbs outside of there, but the rest is pretty arid.
Most people don't really see much besides these two places. There are over 100 islands that have amazing beaches and food and towns, that would be the way to really enjoy it, find one of the less crowded places. Not rush through it to check it off the list, but to relax.