Hi J.,
I am fairly close to you and am a member of the Glastonbury North Mom's Club. I'm not sure if there is one in East Hartford, but I bet there is. If you want to find out, go to the website http://www.momsclub.org. Click on "find a chapter near you/join." From that page, you can send an email asking about the nearest Mom's club for East Hartford, CT and someone will email you back within a few days with the name and phone number of the local contact person. When you talk to her, you can find out what the club has to offer. Both the ones that I've been in have playgroups forming at all times and will set you up with other moms and kids of similar ages. They also have a monthly calendar of events that you can go to and it's all for a small fee that covers mailings etc (like $20-25) for a yearly membership.
You may also want to keep the local access channel on your tv on while you're doing something like fold laundry. I've seen things for Moms in South Windsor and Manchester posted on there. Then, just show up! It's fun.
PS..how old is Brianna...maybe we could get together (mine are 21 mo and 4.5) Good luck.