From the 5th July there are only 3 more games left:
5th July - Semi final in Munich
8th July - 3rd Place play off in Stuttgart
9th July - Final in Berlin
Apart from these cities, i would think it will already be a lot quieter by the time you get there. For example the last match in Cologne is on the 26th of June, so most of the fans will be gone by the time you are here (although it is the base for the brazil fans, so could still be busy if brazil are still in the competition - but the atmosphere will be good)
Like tumbleweedz said, it might still stay quite busy for a week or two after if fans decide to make more of a holiday of it. but even cities like berlin arent big tourist destinations, so i cant picture it being any more busy than Paris/barcelona etc at the height of the tourist season.
Try having a look on a hostel booking page for hostels in the city you wanna go to and see what the availability is like, that should give you an idea of how busy it might be.
"For once you have tasted Absinthe you will walk the earth with your eyes turned towards the gutter, for there you have been and there you will long to return."