Thanks for all the comments. I think we’ll be heading
elsewhere....Appreciate the suggestion about Dresden!
I usually don't recommend Prague anymore since the crowds really have become horrible. But if you want to see "Old Europe", with two teenagers, it's probably the best destination, since all equally beautiful places are much smaller and probably pretty boring for teenagers.
And Dresden? Well, the city offers a small reconstructed old town with many world-class museums, some of them unique enough for teenagers (Green Vault, armory), a lively 19th century quarter on the other side of the river, and a few very nice and posh suburbs with vineyards, castles, beer gardens and so on.
Dresden is a great base for day trips. You can visit beautiful old towns (Meissen, Bautzen, Görlitz, Freiberg... some of them look a bit like Prague in small btw.), castles and fortresses, you can hike in Central Europes most picturesque mountains, there are nostalgic paddle steamers, steam trains, funicular and suspension railways, a village with nothing but Christmas shops all year round deep in the mountains etc..