Obligatory European destinations?

I’ll be passing through Europe in late June, early July, with no strict schedule. I’ve seen quite a bit of France but almost nothing else in the ‘Rope.

Pray tell: where must I go?

This is less “what are some nice places to see and things to do?” and more “what is it a crying shame that I have not eyed in 22 years of eyesight?” Thoughts very much appreciated.