Magnetic Island is about 40 minutes by ferry from Townsville. You can take your own car over on the ferry, or you can hire one there for a reasonable price. Bicycles are also available, and buses operate from Picnic Bay to Horseshoe Bay.
There are a number of spots where nude bathing is practised fairly regularly but due to increased tourism on the island and some pressure from local residents a few have ceased being used. Probably the most popular one is Rocky Bay, just around from Picnic Bay. Either take the track from the eastern end of Main Street, or walk up the road from Marine Gardens to the track directly down to the beach. Balding Bay is another quite suitable spot. Access is gained by following the track from either Radical Bay or Horseshoe Bay. The western end of Horseshoe Bay is also used by nudists. Just use your commonsense and show due consideration for others on the beach.