Taking my daughter to organised play groups several times per week was forced upon me due to needing access to the community nurses who attended, as she needed constant monitoring of a birth condition. However, I'm incredibly glad I went, and continued to do so long after the condition ceased to need such close attention.
I made friends with several other parents, our children bonded and made their first friendships and learnt the basics of social interaction. The shared learning and support we were able to offer each other smoothed over countless daily needs and little fears. Sure, these friendships didn't all sustain themselves long past our kids starting at their various different schools, but by that stage they had already learned so much that I could tell apart many of the children who had benefited from a similar experience and those who hadn't.
I say all this simply to encourage you to try these sorts of groups. You might not make friends who last forever, you might not meet people exactly to your liking, but that's life and it's a valuable experience for the kids for that very reason. People are never more welcoming and friendly than when you have young children and need some companionship, we're all in that same exact boat.