I would caution against using a service like Google Groups for this, actually. There's been too many changes to corporate-backed services like this (Yahoo! Groups' 2010 mess, remember Google Groups was originally a usenet reader to begin with) and moving a community is a pain. Host it somewhere that won't pivot.
We had one for our 'post-college' social circle. It was a good way to spread the word about happy hours and parties, without spamming everyone on facebook.