Hi! I just joined the MOMS Club of Lexington (southeast chapter) last week, because I was looking for the same sort of outlet for my daughter and me. It seems like a wonderful group. The dues are $20 a year, but they will work with you on that if you need help. They meet twice a month as a big group at a particular location (in the southeast, it is at Crestwood Church), and then they have numerous other fun activities throughout the month. This month they have apple picking, pumpkin picking, a day at the Explorium children's museum, at day at Keeneland, park days, etc. They do service projects and help new moms with meals. ALL of these activites are optional. You can do as little or as much as you want. They also have several small playgroups that meet weekly at members' houses. I'm waiting to be placed in one of them based on my child's age, day of the week I can go, etc. Anyhow, everybody has been great so far. I actually bumped into three members at the park yesterday. I don't know where you live in Lexington, but I think there are two different clubs based on where you live.
Here is a link to the chapters:
http://www.momsclub.org/links.html#Kentucky
The phone number to the southeast group is 1-800-728-6931. I'm sure they can help you. Like I said, I'm a stay-at-home mom too, and I joined for the same reasons you're looking for a group. I love it so far. Good luck! Let me know if you need anything else or have any questions.