I promised, here the long awaited post. The below list may not be 100% complete and if you have other ideas, share them! I look forward to your comments.
Your naturist club/campsite/resort/beach
This is the ideal place. No need for a cover up, all you need are shoes, a cap and your GPS.
Country tracks, fields and forests
Depending on where you live, it’s possible that a few hundred yards or miles away, you’ll find hiking trails or forests. This is the second best place. Generally, those trails are not very popular and encounters are not frequent. In case of meeting somebody, you may decide to cover up or not. Some hikers/runners are not against nudity. Ideally run with your naturist mates. A lonely nudist can be seen an exhibitionist, a group of nudist will be considered a bunch of originals.
There are organized races in a naturist club, like for instante the one of Sunny Rest Resort in Pensylvania, and those organised on public places like Bay to Breakers in San Francisco (during which total nudity is tolerated) or the naturist beach race of Sopelana in Spain.
Roads and urban environments
You may run at night or in countries in which urban nudity is tolerated like Belgium or Spain, but you’d better avoid, except if you want to risk to go to the police station.
OK, running on a treadmill does not replace running outside, but it allows a good sweat and endorphins and dopamine discharge, it’s therefore not to discard completely. You should have a discussion between your naturist club and your gym to check if the later would agree to open for naturists once or twice a week. It may allow to use its premises for naturists when turnout is low, but it’s win-win: your gym will fill a low attendance moment and you’ll be able to train naked.
Voilà! Not really complex, but your willingness to run naked should drive you to find a quiet place where you can get naked with little to no risk. I can guarantee that when you find the place, you’ll be ready to do the effort to reach it because nothing replaces a run in the simplest clothing ever, your own skin!