Let me suggest an alternative that seldomly gets mentioned: the public library. It's free, it's quiet, the Internet is fast and not frequently used, the chairs are sometimes comfortable, and they love it when people hang around all day (these are all assumptions of a US base). Additionally, many newer libraries have big meeting rooms with whiteboards and other materials that are free for use. Capped drinks are usually allowed, and sometimes food (don't make a mess!)

It's by far my favorite "coffee shop." Your tax dollars at work.