Social media is a useful tool if you want to find group rides, and they need not be speed-oriented clubs. I joined a local Meetup group of bicycle tourers. I get emails in my inbox all the time about upcoming rides, some of which are longer tours, but most of which are short, local, weekend jaunts. By adding the local Bicycle Coalition and a local walk/bike advocacy group on Facebook, I get notices from upcoming rides there as well. A recent one was a historical tour on bikes, hitting several historical points of interest in my city. Also in my area is a monthly "bike party," where you can join hundreds of other cyclists for a night ride. I discovered this ride through social media as well. I would guess that similar groups/rides can be found in most areas. If not, you could always start one yourself.