Greetings Peter, and congrats on your upcoming travel plans!I'm not sure what particular period of history you're interested in, but here are my tips nonetheless:
The Bayrisches Museum in Munich, a small place at the southern end of the English Garden, has several unique items including one of the only extant covered breastplates from the late 14th C. (illustration 35 and 37 in "L'arte dell'Armatura in Italia" by L.G. Boccia & E.G. Coelho). Definitely worth a look.
The Germanisches National Museum in Nuremberg has perhaps the best single medieval collection in the world. Just my opinion. They have the only great helm that has a mail fringe (probably contemporary w. the helmet) - the "Kornburg" helm (see my online picts – I posted the URL a few months ago on Firestryker) . There are two bascinets and visors in excavated condition, as well as a 14th C. gauntlet. Several shields with original strapping from the 14th and 15th centuries are there as well. A few 15th C. tournament saddles too for those equestrian types. Otherwise the armor is 16th C. and later. They have a large number of home furnishing from the 14th - 16th centuries, (furniture, purses, Minnekaestchen, etc.) including a 1480s living room (Stube) that survived - amazing.
Enough said - it's a wonderful museum and the bookstore is a great place to dump some cash. There is more armor in the schloss in Nuremberg - another bascinet & loads of later things.
The Kunsthistorisches Museum in Vienna would be another "must see", but that's quite a trip from Bavaria - 7 or 8 hours on the train.
Rothenburg ob der Tauber has some things worth a visit. The former convent has been converted to a museum, and it contains the oldest kitchen in Germany, dating back to the 12th or 13th C., if memory serves. They have an armoury as well, but nothing is older than the early 16th C. The town itself is quite beautiful, though it will be overrun w. other tourists in August - don't expect to hear any German. If you do head out to Rothenburg let me know and I'll email you a few good tips on lodgings and the like.
The Deutsches Ledermuseum in Offenbach (near Frankfurt) has literally dozens of small cases and boxes from the 14th - 15th centuries. They only have a dozen or so medieval shoes, but there are plenty of more modern and non-Western displays to please the rest of the family.
If you have time to get up to the Rhineland there's the Klingenmuseum in Solingen and several in Cologne to consider, but this is quite a ways north of Swabia & Bavaria - a full day on the train basically.
Regards
David