If you go to ibplanet.com, one of the moders over there might help you for free to identify what section(s) of code to comment out to remove the registration from invision board. You don't have to buy either IB or PHPBB to modify them. I'll be honest with you though. It's not a good idea to run any forum without registration because you'll be making your boards a sitting duck for spammers and other trouble makers.
Both invision board and PHPBB are very easy to install in any subdirectory or subdomain. Of the free boards, I would say IB is probably the best right now, but I don't particularly like how they've gone to peddling so much commercial stuff. PHPBB is okay. It's a bit more resource intensive. Yabb is okay for very small boards. It will tear up your server if your community grows too big.