Baden Baden

Spas and casinos aren't my thing either.

You could catch the train to Speyer, famous for its cathedral, Jewish heritage, and its Technik-Museum. Figure about 1.3 hours each way:

https://en.romantic-cities.com/cities/speyer/stories/24-hours-in-speyer

One of the quainter towns nearby is Gengenbach, which compares well in some respects with Rothenburg. It's around 35 minutes from Baden-Baden by train, but you'll need to catch a city bus first to Baden-Baden station, which lies outside of town. See this thread for information:

https://community.ricksteves.com/travel-forum/germany/travel-by-train-and-day-trips-from-around-baden-baden-and-mainz

Hiking around Gengenbach:
https://www.komoot.com/guide/3643/hiking-around-gengenbach

To answer your question, yes, you can go off on your own when on a guided tour. There are a few conditions. First you need to communicate clearly with your guide in advance so your absence doesn’t cause a disruption of people looking for you/waiting for you. Second, it is up to you to get back to the group on time for any key transportation times or find your own way.

We went over to Geroldsauer Wasserfall and hiked from the parking lot to the falls and back. At the mid point we had a drink at the cafe. We had a rental car. The path is about 5 miles outside of town.

The current itinerary looks a bit different than when we did the GAS tour with only a free afternoon in Baden Baden. We didn’t do the spa but walked up to the Altes Schloss zu Hohenbaden for the wonderful views. And yes, you are encouraged to make plans to do things on your own during your free time on RS tours. You really don’t need to inform your guide of what you have planned for your free time, only if you opt out of a planned group activity.

I will just mention that as someone who has no interest at all in casinos or gambling, I really enjoyed our tour of the Baden Baden casino. It's a beautiful historic building and was frequented by some interesting historical figures like Dostoyevski.

We walked from Kurhaus Baden-Baden through the Park to Geroldsauer Muhle. This was not a hike, more like walking. I guess, we needed a little bit more than a hour (one way). It was a hot day and I guess the last 30 minutes without shadow. We wore hats, so we‘re fine. Geroldsauer Muhle is a restaurant with german food. We liked it. It was a nice day.

Another short trip was to use the Merkurbergbahn (hill train) . Good view.

In summertime Baden-Baden offers open air concerts and foods. Last year, we spent a weekend the festival at the Kurhaus was so nice. Good music, good food, good drinks and a good atmosphere. Highly recommemded it. You can find the event „Kurpark meeting 2027“here next year, I think https://www.baden-baden.com/

Gegenbach would be great for a full day. For an afternoon agree about touring the casino (gambling not required and quite calm at least during the day) and walking the park, which being a linear park you can get in a fair hike.

There are also some great museums in Baden-Baden. It isn't just casinos and spas. Beautiful architecture and parks.

Thank you all for your helpful comments. We are now looking forward to our visit in Baden Baden!