You'll need a bike to get out of the city and on to Bygdoy - there is a bus, but it only goes to the museums. Cycling through the royal estate, through hayfields and pine forests, you'll come first to a lovely sandy cove at Paradisbukta, and then to Huk, at the very end of the peninsula, where you can swim clad (near the restaurant) or naked (a little further north). A little touch of wilderness 20 minutes' bike ride from City Hall.
Google map: tinyurl.com/34jxyzy
No. 31 buses go to Hukodden as well. First to Hukodden, then the Kon Tiki, Fram and National Maritime museums. (Also ferries to the latter from the Town Hall quay in summer). Agreed, biking is ideal. The beach north of Paradisbukta is certainly nudist, called Honolulu, or Homo-lulu by Oslo humourists (sadly, not many!)