Ours are held in a local family center, it has turned out to be a wonderful location over the years. The family center is a nonprofit, handles donations, services for needy families, but also hosts playgroups from birth-age 5. They have a small kitchen, playroom, chairs, boppys, etc... They refer all women who call or come in with bfing problems to LLL, and often the women who come to meeting start attending playgroups at the center so it works out great for all parties. 
It is just a tiny, little place, but feels cozy.
I've been to meetings held in hospitals, libraries, and homes. I felt that the home of a leader/group member can really put off new moms from attending. The hospital meeting room just did not seem warm and welcoming. The library was eh, they weren't utterly thrilled to have a large group of babies/toddlers taking over their meeting space but it was really the only free location in that town.
If there wasn't someplace around like a family center, often they are not well advertised, ours isn't, then I'd probably go with a church. The big problem I had with a hospital/library meeting room was the dragging of toys to every meeting for toddlers. LLL bought a basket of toys to bring to each meeting to keep children entertained in a huge empty room and I'd have to drag to every meeting. It was SOO nice when we moved to a location where toys were already there and it was more child friendly. Snacks were also an issue with meetings rooms, some didn't have sinks. We were required to vacuum which isn't a huge deal but if you are the only leader like I am and having to bring your own children along then suddenly you just added another huge task to be done. The churches often want you to pick and and leave it tidy but not a mass cleaning like a hospital meeting room.
Good luck!
It is just a tiny, little place, but feels cozy.I've been to meetings held in hospitals, libraries, and homes. I felt that the home of a leader/group member can really put off new moms from attending. The hospital meeting room just did not seem warm and welcoming. The library was eh, they weren't utterly thrilled to have a large group of babies/toddlers taking over their meeting space but it was really the only free location in that town.
If there wasn't someplace around like a family center, often they are not well advertised, ours isn't, then I'd probably go with a church. The big problem I had with a hospital/library meeting room was the dragging of toys to every meeting for toddlers. LLL bought a basket of toys to bring to each meeting to keep children entertained in a huge empty room and I'd have to drag to every meeting. It was SOO nice when we moved to a location where toys were already there and it was more child friendly. Snacks were also an issue with meetings rooms, some didn't have sinks. We were required to vacuum which isn't a huge deal but if you are the only leader like I am and having to bring your own children along then suddenly you just added another huge task to be done. The churches often want you to pick and and leave it tidy but not a mass cleaning like a hospital meeting room.
Good luck!
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