No, I don't think there is any way around it. I am there studying all the time and it is locked down like a compound. The one at Potsdamer Platz (across from the Philharmonic) has a huge lobby, though, with big chairs facing the window. I go there when I don't want to deal with the security.
A good option might be the reading rooms at a university libraries. I sometimes use the Philologische Bibo at the FU in Dahlem. You still have to put your stuff in a locker before entering, but they don't check IDs and the space is pretty nice. You could also try the one at the HU. check out their websites for locations.
One more option would be the public libraries. They are more like an American public library. Low security, kids section, no membership required. I haven't seen much quiet working space though... so I don't know if that is the best option. Here is their website:
www.voebb.de