This is probably too early for your trip but the Rheingau Musik Festival organises concerts (usually classical, some jazz) in atmospheric locations (such as monasteries) throughout the Rhein-Main area in Germany. There are over 150 events. A few years ago I also went to two of a series of concerts which I think was associated with the Festival, where the organiser's ambition was to play all of J. S. Bach's organ music (the entire repertoire, which was spread over the whole year). It was for one of his anniversaries, I don't remember which one, apologies. (If I got any of that wrong, sorry, I'm not an expert.)

Unfortunately, the music festival starts in summer (usually June), so you might miss out this time. Maybe you will have another opportunity to attend in future!

http://www.rheingau-musik-festival.de/rmf,en,home.html

We've gone to a couple of performances in various places in Europe, nothing as off-beat as you mentioned. But we found that the venues themselves were different enough from "at home" to be special - string quartet in a palace in Salzburg; opera (modern interpretation) in the Budapest opera house; violin performance by Nigel Kennedy at the Municipal House in Prague. Set your itinerary, then we what's going on in the towns/cities you plan to visit.

Thank you!

I'recently wrote about going to the Royal Opera house at Versailles.
http://findingnoon.com/?p=810
It was quite a unique experience, even for a local. There is an outdoor opera series in the Paris region, with chateaux as back drops, but I think they start later in the season than your visit.
Opera Garnier is another fabulous place for performance. You can read about it here:
http://findingnoon.com/?p=63

A performance at the Opera Garnier is well worth attending for the beauty of the theatre. We also love the concerts at Ste. Chapelle. Venice has lots of Vivaldi concerts in churches and museums - we try to attend each time we are in Venice. Years ago we went to an organ concert at Westminster Abbey - I don't know if they still have them or not. Try to find a concert at the Academy of St. Martin in the Field if you are in London. We have tried to manage to be in Milan during the La Scala season but have never succeeded. On my first trip to Europe, we saw "Aida" at the Baths of Carracalla with a real elephant.

Check on the opera seasons for the cities you will visit. And check on concerts in churches - there are lots of them, many free.

It's kind of hard to recommend any particular performance as we wont' know if a certain orchestra will be playing in a particular city when you are there. I choose concerts based on the group performning and the repertoire, that's all. I don't really like opera very much so have only gone to that in places where it is relatively cheap (eg, Prague, but you aren't going there).

Other than that, there are many good performances in many good venues in those countries, but many orchestras tour nowadays so who knows who might be playing in one of those places when you are there (could be a US orchestra, for example, the NSO tours Europe, for one, and European orchestras play over here). And you don't even have an itinerary of the cities where you will be, it sounds like.

So in France, which I know best, I would look for performances at the Theatre des Chatelet or Theatre des Champs-Elysees (or Salle Pleyel) in Paris, but there are so many good concerts that are very cheap in all the churches, it would have to be an orchestra I really wanted to hear or a special soloist for me to pay the high prices of a concert hall in Paris. I can't even name all the other places in France, I quite like the OPera National de Lyon, though.

In the Netherlands, I think a performance at the Concertgebouw is usually rather special. I agree with something at the OPera Garnier in Paris as it is a beautiful hall, but I wouldn't pay the prices unless it were something I really was dying to see. I like the Orchestra nationale de France, but who knows where it will be when you are there.

I think you need to figure out your trip first, and then when you have dates you will be some place, look online for concert schedules of the well-known concert hall, or opera house, if you like that genre.

the opera house in prague is truly special. small and gorgeous and memorable. see what's playing when you're there.