Speaking as a BUD person, I'd recommend Berlin. It's close to Prague, and since you only have a few days it seems to make sense. Trains between the two are pretty regular and quick. (Or, if you really want to fly, try and get something going into THF, a beautiful airport right in the middle of the city).
Check out Libeskind's Jewish Museum, a really powerful place, and an amazing example of the ability of architecture to create emotional impact. You might have had enough of Egypt by this point, but there are great collections of Egyptian antiquities in the State Museums, plus the Pergamom collections. If you do like architecture (which I do anyway ) also take time to see the Church of the Reconciliation, built after the reunification.
have fun!