Heavenly, I think it sounds like a wonderful idea!! I had been longing for a local LLL meeting since before ds was born (the one that had been meeting here shut down for various reasons about a year before I had him). When he was about a year old, I finally decided that SOMEHOW, I just HAD to figure out a way to become a leader myself, just so that there would be a local resource!
I started calling leaders in the surrounding towns, and found out that just a couple months before, a Leader had moved into the area and was getting things started again! In fact, the first meeting of the new group was scheduled for the very next week! Yaaay!!!
So, I still have thoughts about becoming a leader at some point, but now I don't feel so desperate about it, since I can tell other moms "hey, there's this great meeting--you should come!"
Anyway, enough rambling!
WRT where you could start holding your unofficial support group (until you are able to make it official--I agree that the support, structure, and reputation of LLL would be very beneficial, but until that's possible, ANYTHING is better than NOTHING!!)....anyway, some possible meeting places (just off the top of my head) might be:
Do you have a local Women's Club?
A community/rec center?
Maybe the Moose Lodge or something would give/rent you space?
A conference room in a hotel?
A local public school? (I know that an elementary school near us has been renting space to a small church that has just started and has no building....I can't see why they'd bat an eye at renting to a support group like you are proposing!)
The problem with all these suggestions is that none of them are free
and someone--probably you--would have to foot the bill! You might consider just getting the word out--like a newspaper add, flyers hung up in Women's Gyms, health food stores, Walmart, etc.--and see what kind of response you get. You just might hear from someone who has a solution, like a conference room at their place of work that they could get permission to use once a month.
If nothing else, if weather permits, you could maybe meet in a park while you try to get better accomodations. I hope this helps, and I hope you have great success! Let us know how it turns out!