I'd hang out in Belgrade.

My husband and I are beginning to feel surrounded by tourists in many of the major cities in Europe. (Yes, I know we're tourists, too, but...) London used to be my favorite city in the world; we were there in April of 2004 and everything was jammed. I can't imagine what it would be like in the summer. We're starting to cast about for less-traveled places. Just made our 3rd trip to Edinburgh, loved the Orkneys, also love Prague and Budapest. Not that they lack tourists, but they're not on the usual London/Paris/Rome itinerary of the package tours.

Without even knowing what there is to do in Belgrade, that would be my choice. You might want to find an interesting day trip by train from there, too.