You can try, besides libraries, church halls, scout halls, service club rooms, public (government) space - but make sure you ask for some sort of support, like free rent to begin with, at least.
Just to begin with, why not meet at each other's homes on a rotating basis? It keeps things informal and fairly equitable. As things grow you will have more idea of where you want it to go. Chances are, once you lose the initial rush of, "Wow! I'm finally talking to someone at last, I want to drink in all the information," you may find the need for weekly meetings wears off.
Support groups also need vital ground rules.
1) What we talk about in the group, stays in the group. No gossip. Confidentiality rules.
2) No put-downs, only support.
3) Allow everyone equal time to talk. Try and limit it to one person talking at a time.
Warning: when a NEW support group starts, this rule may need to be ignored for a while, or maybe set aside some "everybody can talk at once for a while" time. A support group I helped start once, we spent the first five meetings with total mayhem, everyone talking at everyone but still coming away feeling that we had had a chance to vent and still be heard. Later, we quieted down.
4) If you have social get-togethers with family, the support group members are NOT allowed to talk 'shop'. The family members are allowed if they choose to. Or not. This can be a very interesting thing to try.
Any other rules - basic legal stuff, relevant to the laws in your area (such as no defaming various doctors you've found you loathe - find a discreet way to warn someone off the local ratbags.
You needn't start big - small is often best. Informal is great, to begin with. Then let the group go where it wants. You can never try to drive a group - it will drive itself. If you try to drive a group where the members don't want to go, you will fail. If the group is desperately needed, it will run under its own steam. It just needs some steering to keep it on the right side of the road once it's up and running. While you can't choose the destination, you can at least drive it safely.
Good luck!
Marg