When my wife and kids are off somewhere and I'm stuck at home I'm pretty much bored out of my mind, can't imagine being home every single day with nothing to do.
I guess you could do some house work, pick up a hobby, start some home improvement projects. I think I wouldn't have a problem passing the time, my biggest gripe when my family is away is that I miss them.
If you're not used to free time, especially when there is nobody to share it with, it can be hard to adjust. I like to have a few things lined up that I can join in with as and when I'm free. Some friends play chess a couple of times a week and I can always drop by for a game.
Enjoy the boredom. I think if you relax you'll find the inspiration to do something that will keep you motivated and productive. You may find yourself wanting to learn something new or maybe do some virtual freelancing. You'll see that it will all work out.