I'm not too sure. At that point, it seems like taking a long walk off a short pier might be better than slowly going mad. But barring suicide, here's probably what I'd do, if I absolutely knew that there was no chance of finding another human on Earth.
I would have to relocate, first of all, because I really shouldn't be next to any nuclear power plants. Without monitoring, it seems that eventually they'll go critical? I'm not sure. Since I don't know, I will go somewhere nice and comfy, somewhere with less humidity and standing water, so there aren't tons of mosquitoes. Somewhere that gets cold in the winter, so fewer bugs.
First, find some food, and also some seeds to plant. Growing plants is therapeutic, because I like taking care of plants and animals, and it provides a sense of achievement when my plants produce edibles or flowers.
Find some animals, then. If all of humanity just vanished -- no big all-destroying war -- then their pets are still out there. They'll need taking care of, so at least I should adopt a few. If I set up shop in the country, I can adopt some cats and dogs and even probably a couple horses. I will find the smallest, most efficient car I can get, and a work truck for important large tasks, and I'll raid houses for as much money as I can find (to buy gas at the automated pumps, pretty much). With that, I'll swipe whatever supplies I need and basically set up a country farm.
While the electric grid is still up, I'll raid Wikipedia and as much of the Internet as I can, and transfer as much knowledge as possible onto hard drives. I will then collect these and put them in a safe or other locked-up vault and hope that some future race discovers it.
If I'm truly desperate, I could try to recreate some kind of humanoid race by reproducing with the most advanced apes I can find at the zoo. I'm not sure I'd ever stoop to bestiality, but who knows what would happen if I'm desperate and going nuts from lack of human contact. I might also die in childbirth, or have complications, or whatever, so yeah.
Eventually, I'll either start becoming feral and treating the animals as my family and friends and peers, or I'll go quietly insane. Yep.