I joined an amateur theatre group, took small parts, made props, produced plays and, finally, having thought I could never do it, directed several plays. You could also help to build and paint sets, shift scenery, work on the sound and lights, make costumes (or trawl the charity shops). I have made some great friends - you work together for a common goal and if the production is successful you are all on a high, and then you get to party!
If you like singing, how about joining a local choir or orchestra? Perhaps there are Art Appreciation courses.
Or, perhaps join a running group (you need not be marathon woman, groups are diverse and you need go only as far or as fast as you wish). Do you speak any foreign languages? If so, perhaps they are rusty, so you could go to an evening class to brush up your conversation. If not, you could learn one. I did that years ago and we used to go to Paris for weekends sometimes and had such a laugh.
If you can knit or sew, I have heard of 'stitch and bitch' sessions!
It's not always easy, making new friends after a break-up (voice of experience) but it can be done. It may take a little time. Good luck.