I visited today and even though it was windy and a little cool, it was perfect. People were nice and there was little to no clothing on most. I finally took part myself and lost the clothes for a little bit. I wish I lived closer, I would be there all the time.
From what I understand, the weekdays are quieter than the weekends so less chance of offending someone. That being said, this is a state park and there are laws against nudity in state parks. If you are going, please act with discretion so there is no knee jerk reaction to the few quiet people there who do disrobe.
If you are looking for a group of nude sunbathers this does not look like the place - you may be better off hitting one of the local nude campgrounds or making the trip to Mazo.
As for the location, at the south unit, hit the beach and head south. There is a nature center parking lot with a trail to the beach (again, head south). Get away from where textile sunbathers gather. Then be careful! look for others and keep an eye out for the rangers.
Do not pass the dead river, they have posts and stuff marking it off. Read the rules posted in the parking lot and abide - no sense in attracting unwanted attention to your self.
Today the weather was not optimal: Strong southeast wind, and more overcast than was predicted. The south unit was nearly empty, but not quite empty enough (couples kept almost getting too close and then stopping, which meant I kept covering up needlessly).
North unit was, as always, quite empty, but the usable parts of the beach are slim due to erosion -- either wide scoured areas with no cover, or cliff-like with no real beach. I think I have a new favorite cove, though. The sun came out for about an hour or so and it was quite pleasant, but it didn't last. But for that time, I was able to lean back and enjoy the sun undisturbed.
After Saturday's poor weather, I decided Sunday was do-over day.The north beach had a couple dog walkers early, but I found my new favorite cove and spent a few hours without anyone coming anywhere close to me. A quick lunch and I checked what was going on at the south beach. It was sparsely populated -- a few thongs, but nobody nude. There was a couple that was in a relatively secluded spot, and I asked if they'd seen rangers. They said yes, and I replied "So I guess it's not a nude beach day, eh?" They laughed which I thought was encouraging. I settled down a hundred yards from them, hoping they might relax and start a bit of freedom, but no dice -- I don't like being the first. I couldn't stay long, so if the scene changed after 2PM I wouldn't know.
The north unit will still be easy to get into from Hosah Park (by the power plant) or Winthrop Harbor, but don't try to "sneak" into the South Unit. When they were closed for most of a year due to huge numbers of fallen trees a couple years ago, I got chased out by a ranger when I tried to get in using the bike trails.