The most local one to me is Borealis Yarns - it's less than two blocks away! They've got a nice stock and a table for people to sit and knit. There's a coffee shop going in next door soon. They are quite welcoming to my 16 mo DD - when the owner offered me a job, she made sure to say that my daughter is welcome to join me.
There is also Three Kittens, which I worked at while I was pregnant. It is the most well-stocked yarn shop I've ever seen, and the owner knows more about random yarns than I can fathom. She's expanded fairly recently and now has a couple chairs for people to sit in. It used to be just some folding chairs around the table and not much room to just sit for a while.
There's also Depth of Field. Another well-stocked shop. They also sell fiber for spinning and coned yarn for weaving. Their sale loft is fun to check out. The owner and her employees are so friendly and it's nice to just go chat.
There are so many more yarn shops here (I think there are like 13 or 14!) but these three are the ones I'm most familiar with. None of the ones I've been to have sofas or anything to sit in, but they've all been pretty welcoming. There are one or two where I've gotten a cool reception, and unfortunately I'm not the only person who's gotten that.
Most of them are great, though.
I'm in St. Paul, MN by the way. Both Borealis and 3 Kittens are in St. Paul, Depth of Field is in Mpls.