Supposing you don't have the money but must get someone who lives close by a gift, what would you get them? I've heard it said that offering some "free service" is a good enough gift which anyone will gladly accept. For example you could offer to babysit if a neighbor has kids, offer to walk their pets for a week or longer, etc. All you need is a little bit of time.
My mom's best friend gave her a free carpet cleaning as a Christmas gift. She already had the equipment because she owns and manages a number of rentals. It was very much appreciated.
I helped a friend organize her messy place and I helped her clean. I guess my free gift to her was to be her free maid for a day. I was glad to help. She's a single mom like me and she's busy.
I do like this idea. I stayed with a friend in California a few years back, and I helped her clean out her closet while I was there. Had to make room for our shopping trips, haha. I know she appreciated the gesture, and it pleased me because I enjoy cleaning and organizing.
I have a pile of items I got as gifts that I never use and I usually just get from that bin whenever I need to give out a small token gift for others. I know it sounds bad but I never would use those items otherwise so I think it's okay to just regift them. I think this is the best way to give out free gifts on smaller occasions or regular days since it doesn't require much time or effort.