My experiences with this difficulty come from two things; my experience working in a nursing home and our experiences with our elders in assisted living. This article will be more about how to choose a gift than what gift to give. You can also discover the best games for dementia patients from the web.
Space: Unless the person is in a private room there are going to be space issues. Even a two-bedroom will have some of this difficulty. An example we've had to cope with is our elder's television set. It was a gift, and it may turn out to be a problem. You see, it's a 60-inch set and not all single rooms are set up for something that size.
On the Ward: Hospitals, nursing homes, and some skilled care facilities have wards as well as rooms. In award there can be a dozen people. Not only is there a big space issue there is a "people" issue. What if someone in the ward doesn't like it? What if they like it enough to "borrow" it? What if someone is jealous? These issues are even worse if the ward is part of a dementia unit.
Medical Conditions: This in part goes back to the ward and shared room. Another of our elders is extremely allergic to just about every scented item known to man. Was she in a facility in a shared room or ward she would have a severe allergic reaction to flowers and perfumes? It's wise to ask before giving this sort of gift if your elder is sharing a living space.
There are also things that people with medical conditions can't eat. Bringing a diabetic a pound of chocolate candy isn't wise. Talk to your elder's doctor about food and other restrictions before selecting a gift.