Best island if visit only one

My husband and I are leading a group tour in mainland Greece in July. Before the tour we would like to spend a few days relaxing on one of the islands. I’m thinking I probably must go to Santorini, but I don’t want to be overrun with tourists. We are looking for beautiful, relaxing, romantic scenery (oceanviews), some good hiking trails and awesome food. We will fly into Athens on July 8 or 9 and then need to be back in Athens on the 12th. Which island, or islands would you recommend for our 3 nights and how should we get there?