There aren't many community hospitals with neuro residencies at all. With that said, there are many mid-tier residencies that really don't care much about research on the part of residents (much more care for faculty). I personally don't enjoy research at all, and have largely been able to avoid it in residency and fellowship. The research is there if you want it, but you are not forced to do it. One or two small pubs is already enough to match neuro/have something to talk about in the interview so you don't need to do much more particularly with how busy third year gets in med school. Fellowships in neurology are not competitive overall, and you likely won't need to do much if any research to get one. It is even possible to get name brand fellowship spots without research (or maybe a small project in process). Going from mid-tier residency to name brand fellowship (and vice versa) is not uncommon either.
FM, PM&R, gas, and path attract vastly, vastly different personalities than neuro (and different from each other with little overlap). Make sure this field is what you want to do with your clinical rotations.