We highly recommend the Rodies Villas hosted by Lea and Lisbet It's a wonderful place to stay on Folegandros, just a few minutes walk to the Chora with fantastic views of the church overlooking the town. We really liked the overall modern-farmhouse like style of the home. The house was a little crowded for our family of 4 (kids aged 19 and 12), but that was to be expected given the kids were sleeping on the two beds in the living room. The bed in the bedroom was very comfortable.
Lisbet was very responsive, picking us up at the port (monitoring the late ferry), and dropped us off to catch our departing ferry (which was also late). She offered up a number of recommendations, and quickly resolved an issue we had with the water.
The patio was our favorite place to hang out when we were home. The view eased the pain of having to work a few times while we were there. The internet was ok for video calls and other remote tasks (not the strongest, and occasionally unstable). Bring a sweatshirt or light jacket, it can get a chilly in the evening, especially if it's gusty out.
It sounds like a contradiction, but Folegandros is a great laid back island with a bustling Chora filled with numerous atmospheric dinning opportunities. A car is not necessary, you can take a bus and then boat/hike to a number of great beaches. We did rent quads one day, which was a lot of fun and allowed us to easily explore some of the beaches on the far west of the island.