of course you can camp in or around major cities. Most likely it'll take you half an hour or so to get downtown, but that's worth it, isn't it?
I've camped in Berlin several times. I always stayed in Gatow, which is about 45mins by bus from downtown.
The address is:
Kladower Damm 213-217
To get there, take the Bus 134 (or 334, X34) to "Kladower Damm", from there on, there are sign showing the way.
I think I payed 50 Euros for 4 days of camping, I had a three-people tent on a fairly large ground.
There's another great one which is closer to downtown Berlin. I haven't camped there yet, but the www-address is: http://www.hettler-lange.de/p2/en/deauswahl.html
That one costs 8 Euros a day for the tent and the person itself, that is cheap. Showers are 1 Euro, that's pretty much normal.
To find campsites in the other cities, I advice you to use good old Google machine.. It finds a lot.