Last minute trip to Frankfurt May 27-June4

Are you arriving in Frankfurt after taking a trans-Atlantic flight? If so, don’t rent a car after a night of no sleep. The drive you’re talking about takes 6h and 15m and you won’t need a car while in Prague. Lufthansa has a round trip nonstop flight on Sat. May 6 departing Frankfurt at 12:25p and returning from Prague on Tue May 9 to Frankfurt for $456 per person. I highly suggest buying two tickets. You can then take a train from Frankfurt airport to Heidelberg (1h 15) that requires one transfer.
Rent a car in Heidelberg and drive to Rothenburg ob der Tauber along A6 (2h). The A81 takes 2h 30m. Another good day trip is Baden-Baden (1h 15m). I'll let Russ take it from here, but he'll probably say skip Rothenberg and Baden-Baden.

IMHO Prague is both too far to drive (WAY too far) and too far to take the train. After a red-eye transatlantic flight when one or both of you may be fatigued, treat yourselves better.

What will you do with a car in Prague? I really can't see any reason for it aside from leaving it parked (for a fee.)

I would plan to leave FRA at 10:34 for Nuremberg on a direct train (arrive 13:27,) check into to some pleasant hotel not too far from the station, attend to my personal needs (probably a hot shower and a cold beer aside something tasty in one of Nuremberg's nice pubs) and then take a stroll through the old town zone and/or take in a museum while trying to stay awake until at least 8 pm or so.

I'd wake up too early, probably, but refreshed. Then I'd hit the station for Frühstück and board the 7:38 so as to arrive in Prague at 12:17 (1 chg of train in Schwandorf.)

The fare for both trips at DB right now, on one ticket with an 18-hr stopover, is €69 each. (Gas alone, for the sake of comparison would total up to roughly the same amount.)

After thinking about the punishing drive you have in mind, I'm too pooped right now to think clearly about the rest of your journey. Maybe tomorrow.

In the meantime, what sorts of interests do you have that might help determine what to see/do on your way to Heidelberg?

AFTER PRAGUE: On Tuesday morning... take a morning train to eiither Bayreuth or Regensburg for car pick-up. Bayreuth is a very nice place with enough things of general interest to choose from. The Markgräfliches Opernhaus is on the "twee" end of things, with Maisel's Brewery tour on the other. I suppose your impending drive to H'berg might interfere with the latter, however. Bayreuth lies toward the eastern end of the classic "German Castle Road" (Deutsche Burgenstraße) which takes you to Heidelberg eventually. I don't thing it's drivable in a single day, so you might target certain stops that interest you, opting for faster driving routes on either end of those stops. Do some research to see which stops are most interesting.

Regensburg is a UNESCO World Heritage Site for its well-preserved medieval old-town center. Driving from there to Heidelberg could involve some of the Burgenstraße towns as well.

As for your final nights... hard to say. You had Eltville in mind, but your intentions there aren't obvious. Maybe you were planning to day-trip into the Rhine Gorge from there? If so, it could make sense to just stay in one of those places and use your car to explore the region. You say you're "familiar with most of these places" but I'm not sure which place names in your post you already have under your belts, or whether your travel experiences include Rhine, Mosel, Lahn, and/or Nahe River destinations (where there are several "hidden" gems, and one town famous for its gems, actually!) - or whether you wish to visit new places or just return to the old ones you already know.

With a 10:30 morning flight, I would make a point of staying in Mainz the night prior. From there, 2-3 direct trains per hour head to FRA airport in 20-25 minutes beginning at around 4 am. Mainz is a great town with a large pedestrianized town center where you can wander around, see a few sights, do some final shopping before heading home - so maybe arrange a few afternoon hours there on your Saturday as well.

Thank you so much for all of your input and suggestions. I have already researched the flights and train options on all fronts and am most comfortable having our own car but I will give it serious reconsideration.

Regarding Heidelberg, I am an avid hiker and generally love anything outdoors.

So, post Heidelberg, was looking for fun relaxing hangout town that is still fairly close to Frankfurt but easy to explore other towns, castles, vineyards, or unique experiences like the falconry show I read on someone's thread.

For comments from several forum members on the wisdom - or lack thereof - of driving right after an overnight transatlantic flight - for less than HALF the number of hours you'll be facing - the recently-opened thread below may be informative:

https://community.ricksteves.com/travel-forum/germany/driving-to-rot-after-flight-into-frankfurt

Look into Boppard, Rüdesheim, Wiesbaden, Limburg-an-der-Lahn, and Mainz as post-Heidelberg base-town options. Travel time to FRA will vary.

Although it is a long trip report, you may find some useful material in the Fachwerkestrasse section of this trip report:

https://community.ricksteves.com/travel-forum/trip-reports/baltic-germany-fachwerke-landesgartenschau

Here is one recent discussion of housing outside Frankfurt. But I refer you back to the first link, where I mention problems getting to the HBF (not even the airport) first thing in the morning.

https://community.ricksteves.com/travel-forum/germany/where-to-stay-outside-of-frankfurt

I don't make a particular point of warning people about driving after a night of poor sleep on the Transatlantic plane. But your insistence on a car for a drive between two major cities of Europe seems [American ... ] eccentric. It's no pleasure, and it carries few benefits. We spent several nights in Prague, which can't be seen "in a day", and I felt no desire for a car. It may not apply to Germany-rentals, but when I once rented a car at the Zurich airport, I was ordered not to drive it to Czech Republic. Luckily, that wasn't my plan. Driving and parking a car in medieval street plans (and tiny commercial garage stalls) is no fun, especially with (say...) a big, high-testosterone BMW or Audi.

In my experience with Lufthansa code-shares from the U.S., we have gotten second-segment flights to other cities in Germany (did not try Czech Republic) for virtually zero additional dollars. (That was for the initial purchase, not a change or add-on.)

Again, thank you for taking time to give me your input.

We are booking our flights to Prague.

So I am rethinking our time after Heidelberg. We have spent the majority of our Germany time along the Rhine river between Essen and Trier and the far south in the Bavarian Alps. So, after reading your thoughts and links, I really like the idea of exploring the Bergstrasse. This is an area we have not spent any time. How would you budget your time from Thursday night, Friday and Saturday? Biergartens are a must. Really like the idea of hiking one of the trails near Burgensteig and possibly fitting in a visit to Gross-Umstadt. Would love to hear your thoughts.

We didn't have the time for real Bergstrasse driving or strolling. But I think some other posters commented on mentions of that name. Maybe you should try the term Bergstrasse (and Bergstraße) in the Search box top center/blue menu here. The Search function works pretty well. Remember that hiking is almost a religion in Germany!

Bergstraße visitors information:

https://www.diebergstrasse.de/en/holiday-route-bergstrasse/

"We have spent the majority of our Germany time along the Rhine river between Essen and Trier"

?? Neither Essen nor Trier is a Rhine River town. Trier is near the border with Luxembourg and has around 200 km of Mosel River between it and Kobenz, where the Rhine is. I'm unclear about what you've seen on the Rhine, and it sounds like you may possibly have missed the most scenic part, which lies south of Koblenz between St. Goar (near the Loreley) and Bingen. See orientation map.