No, the laws don't vary but it's not so easy nonetheless. When you're in your garden and no one can see you (because of a big fence, probably) it is okay.
It's a different case if you wanna go hiking or for a walk (naked). You can do that in an unpopulated area as well as in the center of a city. Technical it's not forbidden or illegal. It all depends if OTHER people take offense of it. When you're in the middle of a forest, you might not even have to pay a fine and just get a warning.
If somebody takes offense, because you do it in the city and calls the police, you probably have to pay a fine and get "banned" from that area. But no one would arrest you or something...
I can't recommend any places because I'm not into that stuff, sorry.
But there are a lot of beaches in the north (east) of germany where fans of "FKK" go. Basically those are beaches like everywhere else accept everyone's naked there, lol.
Summary: public nudity is not illegal, as long no one else is taken offense of it. The worst you have to fear is a warning, getting banned from that area, and worst case scenario you have to pay a fine.