Papa Playgroups: An Idea that Shouldn't Only Be for Hipsters

So, my husband really has only one dad-friend. There are only a handful of people our age and/or in our social circle who have children, and even fewer with kids Stenni's age. Even then, most of those dads are less than super-involved with their kiddos, except for the ones with very little babies. It's sad, I know, but it's life. Even friends of mine are surprised when the hubs takes Stenni out on what they call "ballerina dates" (they both get dressed up and go wherever she wants, usually every Wednesday night) or puts her to bed by himself or does anything else that I think a reasonable partner should be expected to do, at least occasionally.
So in an attempt to make a few new man-friends with kids, we started looking into finding a "dads group" for playdates. Guess what we found? If you guessed nothing, you're only half right. We found a ton of moms groups within a 20-minute or so drive, but not a single dads group. Not one. Then when we looked a little further away (closer to NYC/Hoboken area) there were a few...for stay-at-home dads only, held during the day. So an employed dad who wants to spend some extra time with his kids has very few opportunities to do so in that kind of setting, unfortunately. I find this kind of ridiculous, because there are working moms playgroups for women who work all day, groups only for stay-at-home moms, and groups for stay-at-home dads...but what about for the work-a-day breadwinning father? I know that they are a rarer breed in this day and age (rarer still are the ones who want to spend their precious free minutes with a group of other dads and kiddos), but come on! We didn't even find a single "parents group" either...most were moms only and a few were dads only. I'm not a moms group kind of gal...I've tried a few, and they're just not my bag, for whatever reason. I don't like to socialize based entirely on my kid, and I have very little else in common with most of the other moms I've met in these groups. But for my husband I think it could be different. In a dads group, a man already has more in common with the other men in the group, namely that he's the type to take a serious interest in his kids' lives. The dad groups we did find, too, were of the super-hipster variety, who want to crucify people for "unapproved" life choices (think those types who only eat vegan and organic, who only wear organic cotton and drink fair-trade coffee, you know who I mean...we try to be conscious but come on!). Like Brooklyn on steroids type dads, who scoff at competition amongst the kids, chafe at hubs' traditional job and schedule, and are aghast at the idea that I stay at home instead of striving for equality in the public sphere. A playgroup should be fun and social, not a platform for pushing (or needing to defend) life choices.  
Anyway, because of this hubs is thinking about starting a dads group in our area, but with everything else that he has on his plate, who knows? I kind of hope that it happens, as he could totally use some more male socialization outside of work (since he works at a women's prison and we have a toddler girl, he's always telling me that he's tired of dealing with misbehaved women all day!), and that way I'll have to trek to the park a bit less. Any suggestions?