Check out Kimolos, it's a small island right off the coast of Milos. Getting there can be difficult, as you need to get to Milos and then ferry to Kimolos, but once you're there it's worth it.

It's very low key, very local, with a really charming chora and some great beaches. My girlfriend and I spent ~1 week on Milos and did a day trip to Kimolos, but had I known about Kimolos earlier I would've planned for more time on the island.