If you have more time, consider taking a day trip to the island of Delos. It's a significant archaeological site and UNESCO World Heritage site. Another beach to consider is Super Paradise, known for its beach parties and lively atmosphere. If you have less time, you can still explore Mykonos town and one beach on the island. When you're walking around Mykonos town, be sure to bring comfortable shoes, as some streets can be steep and a bit challenging to navigate.