It costs $150 a year to run a group on Meetup. It doesn't cost anything to join groups, though individual groups sometimes charge dues to cover the yearly cost. Depends on the group, of course. We were having trouble scraping together dues, so we left Meetup. There are only about eight of us who are active, whereas the group had almost 100 members on Meetup. So fuck that.

Google has everything you need to run the same type of group for free, as you suggested. We use Google Calendar to schedule events and we have a blog. It's a little more work, but that's fine. For now.