My vote is for Central Europe, in particular Germany, Austria, and the Czech Republic. Summer is such a beautiful time there and the weather is perfect for enjoying anything outdoors. After all, it wouldn't be summer in Central Europe without some opportunities for hiking - a great way to meet local tourists! The region is full of fascinating history and delicious food and, particularly in Germany and Austria, the public transportation infrastructure makes it easy to go out into smaller towns and villages and experience local culture. It's also surprisingly affordable (outside of Vienna and Prague) compared to other parts of Europe - I'm always delighted by how far my money stretches when travelling there compared to Northern or Southern Europe.
My ideal itineraries would be:
Prague->Bohemian Spa Town (Karlovy Vary, Mariánské Lázně)->Dresden/Saxon Switzerland->Berlin
Prague can be hellish in summer, hot and crowded with tourists, but if that's the only time you can visit then you may as well brave the crowds. It's always worth visiting, regardless of the season.
I also think a great summer trip could be spent between the Black Forest (Baden-Baden and Freiburg) and Bodensee (aka Lake Constance) but that would be very outdoors-focused, rather than on culture. There is certainly lots of history, though (especially around Bodensee - check out the museum in Unteruhldingen, which looks back to the way people lived there in the Neolithic era).
Have fun with your planning!