Ulm is 1,5 hours away from Stuttgart; you change trains once, in Stuttgart.
In Ulm, you will visit the Ulmer Münster of course. If you are technically interested, you might try to arrange for an audience with the director of the Ulm proof office, which is only a few foot minutes away from the MSZ.
Also, I encourage you to acquire a state shooting medal for hunters there (Landesbüchsennadel, Landeskeilernadel). It is not really difficult, and will add some flair to your US hunting outfit. Can be worn on the hat or on the breast:
https://mszu.de/schiessstaende/schiessnachweis/See the pull-down menus.
If you are a member of the German Gun Collectors Association, you must see Mr. Warkus at Frankonia Jagd in Stuttgart. He is the last scion of the Eblen family, the famous Waffen-Eblen.
For Germans, that once was one of the great firms and gun houses of national repute, like Barella, Otto Bock, Foerster, Lueneburg... For Americans, they purveyed guns to Hermann Göring.
And if you want to invite your in-laws to dine out, it's Malathounis in Kernen-Stetten. The cuisine is unique, the Michelin star merited. The wine list is among the best and most interesting in Baden-Württemberg (only the Alte Weinsteige in Stuttgart has a deeper one), and you must try a bottle of Hatzidakis (Santorini).
Regards,
Carcano
