If you don't fancy the idea of volunteering, and can't afford a trip away, then I'd recommend thinking about some of these things.
Make sure you get out of the house each day, even if it's just for a walk. On Christmas Eve, I can highly recommend a trip to the local swimming pool. Most swimming pools are really quiet on Christmas Eve, so plenty of room! Then maybe treat yourself to a nice coffee or pub lunch.
Christmas Day is the hardest, as nowhere much is open, and most people are doing family things. I'd make sure that as well as a walk, you have a pile of nice things to do. For example some good books to read (these can be from the library if you're on a budget), and if you have any hobbies you can do at home, then maybe a new project to start. Get some nice food in (something you like yourself, it doesn't need to be "Christmassy"), and listen to whatever you like (radio or CD/download) or watch what you like on tv.
Boxing Day, aim to get out again, and maybe see if you have any friends who would like to come round in the evening. Lots of people are totally fed up with their families by the end of Boxing Day, and welcome a change of scene/company. If money's tight, suggest that everyone brings a drink and a plate of food, and you'll have an instant buffet.