Any outstanding restaurants in the Rothenburg, Heidelburg, Mannheim, Schwetingen areas?

Have you checked the Michelin guides/ratings?

I love to look for the daily specials menus while walking around towns. I know you want spargel so make sure they have it for the evening meal. I love dining outside if weather is nice and many towns have options like that. Trip advisor has good reviews of places just take with a grain of salt some reviews. I could care less about Michelin stars so look for what sounds good and the dining options.

Michelin's red guide (hardback and online) deals with ALL kinds of restaurants, not just starred ones, and its recommendations are usually excellent.

We were in Rothenburg in September and had a fantastic dinner at Zur Holl. Definitely make reservations! We also had a very good lunch at Gasthof Goldener Greifen on their back patio. We had a dinner at Restaurant Michelangelo one evening and while the food was fine, I do not recommend it. The waiters had no idea which tables were theirs, if orders had been taken etc and they were pretentious. This was an anniversary dinner, but we left as soon as we were done with our meal, skipping dessert and more wine as we just wanted to get out of there, FWIW.