If looking for a place to go swimming or other such activities then this might very well be the place for you.
Legend has it that when the widow of King Gustav II Adolph fled from Sweden in 1640, she was first taken to Nåttarö where she found shelter in a cave while waiting for a vessel that would allow her to escape. Also, August Strindberg immortalized Nåttarö in his painting of the Queen's Cave "Inferno".
Exploring the countryside is easy due to the lack of cars, and if you're staying a few days then renting a cabin is as easy as it comes, just remember to book ahead.
You can get to Nåttarö, by taking the Waxholmsbolaget (Swedish link)(+46-8-679 58 30) ferry, which leaves from Nynäshamn harbor (which you get to by the commuter train). Cabins can be rented through "Din Skärgård" (+46-8-744 50 01)
Photo: Jeppe Wikström