I really like Riiley's suggestion of a little bit of both: hang out with Bebe Extraordinaire for a bit, then "Hey, Mama needs some me time. Let's go get dinner!" or something else.
I personally didn't have a huge problem with this; then again, I was 36 and my husband was 44 when we had our son. Most of our friends are older (in their 40s, 50s, 60s) and childless by choice, so while we didn't hang out with them as much, we do have the benefit of getting a lot of odd encouragement in the form of compliments like "Your kid is cool. He's not weird like other kids." (this from a very brusque dear friend, who likes that Kiddo's "not a freak, and actually knows how to listen"). For our friends, they were less interested in holding the baby than they are now, as the older guys like to sit and play guitar or blocks or just about anything with him. The Aunties are amazing, too. Not my sisters, who are also great; these are honorary Aunties... the ones that *would* hold the baby. You should have seen the looks of horror on some of my girlfriends' faces when we offered "Do you want to hold him?" Some offer to babysit, some don't, but I know they all know what he means to me and they love him for it too.
One younger single friend sort of began 'recoiling away' when we announced our pregnancy. Without going into it, her personal history made it hard for her to be around us; she'd had disappointments in both love and pregnancy, and I could see why she just sort of receded. I think, in retrospect, it was easier for us both. So, there's another perspective.
I could go on and on... what I'll just say at the end is this: hopefully, with this playgroup, you'll meet other moms you connect with on a personal level, and THEY will be the ones who decide to take you up on a Ladies Night Out sort of excursion. They will understand why you need to get out sans baby, even if it's for a couple hours. One woman in my mom's group began organizing these by the time our babies were about 4 or 5 months old, and now that our kids are 3-4 years old and a new round of babies have come about for some of us, we still meet from time to time. I can't attend the playgroup, so this is my way of keeping connected with this fabulous group of mothers.
Have fun and hopefully, your friends will be able to get their baby fix, and then get out the door for a night out.:)
Best to you~
H.