I want to spend nye home alone saying no to an invite from the neighbors and possibly hurting their feelings
Why will you possibly hurt their feelings?
I don't really want to hurt their feelings but I don't want to go to a New Years Eve celebration either.
If you don't want to go, then don't go. They will not be hurt by it, not everyone they invite will end up going.
It could still be an issue in the future. I gotta think about my plans.
It should not be an issue. It is impossible to go to every event you are invited to. Stay at home for this time, maybe you want to go to another event with them in the future.