OP, any hints about which ideas, out of the ones suggested, sound like they might be helpful?
If I am in a good mood, here are things I might enjoy doing by myself: walking and picking up litter on the side of the road (a hobby of mine), making something like bunting out of old fabric scraps, gathering greenery and decorating the house with wreaths and lavish fresh evergreens (I live in the country), borrowing a dog for a long walk, writing a letter to an old friend, reading for hours in front of a fire, going to a carol service (I am an atheist), painting a room in my house or doing some other big house project while listening to interesting podcasts or a book on tape.
Here's what I would do if I am feeling down: lie in bed for too long, eat too many snacks, stare at my computer all day. These things make me feel worse, but I still do them when I am feeling down in the dumps.
The main thing I want to say though, is that single Christmas visitors are incredibly valued at Christmas in our house, both when I was a child, and now that I have children of my own. We always want to have a few extra people, for purely selfish reasons. Visitors make Christmas feel special and party-like; visitors bring interesting and unexpected presents, foods, traditions, and conversation. The presents might be something small- an interesting old photograph, a taste of some new foreign treat, a homemade card, etc. The conversation is just dependent on it being not what we are used to, day in and day out.
In recent years we have had all sorts of casual Christmas visitors, such as one of our kids' piano teacher, the disabled brother of an old friend who doesn't usually leave his house, a child's foreign friend from college, (stuck in the UK with visa problems), a mum and child with no family left, etc. All of them were extremely helpful to us in making Christmas fun and interesting.