You didn't say what type of "seniors' home" she's moving into...independent living, assisted living or a nursing home...and that makes a difference in the choice of gift. I like the idea of a fabric box although a covered one would be nice...maybe large enough to keep photographs, cards and letters, a crossword puzzle book, a magazine, or other treasures close at hand but out of sight. It wouldn't have to be as large as these though. If desired, you could make a top in the same way, but with shorter sides and a very slightly larger base.
http://www.sewcando.com/2012/03/quil...orage-box.html
A tissue box cover or bookmarks would probably be used often, too, and remind her of your thoughtfulness.