My wife and I are flying into FRA and renting a car (is unlimited mileage an option? Hertz doesn't seem to offer it) Aug 22nd and need to fly to Southampton on Aug 25th. My only requirement is to visit Goppingen (where I was born, have not been back in more than 30 years) other than that I am looking for suggestions on where else to go. We don't need to fly to SOU from FRA and we could always fly to STR instead of FRA on the 22nd.

As for the rentals: I don't rent that frequently in Germany, but I think it's a case of YMMV. For one-day rentals, recently, I've seen Hertz offering nothing but 400km/day and Avis & Sixt 300km/day, but for multi-day rentals, you still can get unlimited mileage more often than not. Even in case you have Hertz status, it might be worthwhile to compare against Sixt, as they are the biggest player in Germany, I think. In the German market, Avis is probably bigger than Hertz as well.

As for recommendations on what to do, you don't have much time. I think Frankfurt is much better than its reputation on FT and well worth spending a day or two. Great museums, historically significant buildings and architecture, nice restaurants, good nightlife, decent daytime outdoor events during the summer. But it totally depends on your interests. Going to the Schwarzwald (Black Forest) for some biking, hiking, and such is an option (small detour on your way to Stuttgart/Goppingen). You're passing by Heidelberg on your way to Stuttgart, so that would certainly be easy driving-wise. Bergstrasse-Odenwald is an alternative to the Black Forest (and closer to your destination as well). I think I prefer the Black Forest for the dining options and cultural highlights in places like Baden-Baden, but Bergstra�e is nice, too. It's also a wine-growing area.

TBH, I'm not a fan of Stuttgart and surroundings and hate the local accent. But if you're into cars, there exist some notable options there as well (e.g., Porsche-Museum, Mercedes Benz Museum). Also, you got some castles, old churches, and such. Dining in Southern Germany is usually also pretty decent. But generally, the stereotype of Swabian people is that they are hard-working, stingy, tidy, conservative, and close to nature. The Frankfurt area is a tad more liberal, alternative, open-minded.

Again, you really have little time. It boils down to your preferences.

I'm more of a Berlin person, however the few times I've been into FRA we've taken the train to Mainz and had a wonderful time. It takes about 30 minutes from the Hbf.

The wife, who's spent a good deal of time in Frankfurt, recommended the German Film Museum and the area around Museumsurfer.

Book via ADAC (German AAA - rentals will be from Hertz, Sixt or Europcar). They let you rent even if you're not a member. You won't get the members' discount, but rates are still excellent and most come with unlimited mileage and zero excess.

The drive down the Rhine is nice.
Off the wall suggestions. Spas in Baden Baden. Europe’s largest amusement part, Europa Park in Rust. Kind of Epcot meets Universal Studios.

Goppingen is near Augsburg, which is worth a day or two visit, historical nice city. Of course, you're not far from Munich which has a tremendous amount of things. If you want more nature, you can look south of Munich towards Starnberger See and the whole region has hills, water, cute little towns. You could fly out of Munich, which is a major air hub. Any reason you want to rent a car instead of taking trains?

MUC to Goppingen is at least a three-hour train ride plus probably a 30 min wait time (trains don't run that frequently outside peak times).

The ICE line Frankfurt-Stuttgart is affected by major track work in August. Trains will be routed through Darmstadt-Heidelberg as opposed to Mannheim. Given Frankfurt-Mannheim is one of the busiest routes in all of Germany and Frankfurt-Darmstadt-Heidelberg does not have nearly the capacity needed, expect major delays on top of the ones built into the DB schedule for August.

Visiting Heidelberg via train in August 2024 during what will with absolute certainty become a major DB schedule meltdown area is a pretty bad idea.

Augsburg is also not that close to Goppingen by train. The train takes between 1:35h and 2:00h. And that only gets you from central station to central station.

A rental seems like the prudent thing to do here, the only exception being flying into STR and not planning on visiting places to the West or North of Stuttgart.