Chur, Bregenz

if I was going by automobile, I would be stopping at Kloister Andechs. It is maybe the best brewery there is, and it is in the village of Andechs

I've been to Chur. Nice enough place to spend a night before the Bernina Express, but I'm not sure I would go out of my way to stay there.

I don't know about Chur - haven't been there, but as far as Bregenz goes - if I were to choose a town on Lake Constance for a stopover it would not be Bregenz - it would be Lindau.

IMO, Chur is worth at least one night. I've spent a couple of nights in Chur, and quite enjoyed touring around. I had some interesting "travel experiences" there. You may find this helpful - http://www.churtourismus.ch/?&L=4 .

Well, I haven't been to Chur, but it was interesting that Google Maps wouldn't accept the name, and substituted Casinos Austria Management for the location!

Bregenz (which I have been to) is right on a major scenic lake, with seasonal ferry services. The town has a major performing arts center, with a stage built into the lake. There was a chase scene in the James Bond movie Quantum of Solace shot there, because of the monumental opera productions they do on the Seebuhne. It would be very crowded in that summer month. I believe (but have not seen or specifically researched) that there is a major scientific (physics?) research center in the general area, that offers tours with limited access and long lead time required.

I haven't seen much of Bregenz. What I have seen isn't particularly noteworthy. There is the stage on the lake as others have noted. If that floats your boat and you can get tickets for exactly the day(s?) you'll be there then that would definitely a big point in its favor.

As for Chur. I have been there a few times. It has a pretty nice old town but not much beyond that. But I've never looked particularly hard. What could make it worth the stay would be a small detour to the Ruinaulta area around Flims and Laax. There are many paths through the forest there going by lake Cauma, lake Cresta and the viewing platform Il Spir. You can to anything from longer walks to short hikes. There's even a horse carriage you can book that takes you from Flims to Conn (the area of the viewing platform)