As others have mentioned, I'd download all of Wikipedia, maps, and every other part of the Internet that I think I'd need. Terrabytes of articles, funny cat pictures, dick pix, and games.
Then I'd become a wanderer. I'd forage in houses for food and treasures. Maybe look for other survivors. I'd spend my down time reading books and becoming an expert on every subject.
I would also continue to deposit my Newgrounds XP every day until it is no longer possible. Then I would travel to the Newgrounds office and edit my account to be level 61, but not before drawing a large, anthropomorphic penis on the wall.
At some point, I'd visit every major landmark and technical marvel, scrawling "Bit wuz here" on it along with another penis picture. I'd be sure to write down what station to tune to in order to contact me. I'd be broadcasting for an hour a day in order to find others who may have been left behind. With my information being spray painted in every town and city I visit, there's a good chance that, if there are any survivors, I'll be contacted eventually.
It would also be pertinent to be protected from the animals who would quickly take over all previously populated areas. To accomplish this, I'd befriend German shepherds and keep a pack of them around me at all times. Not even a fully grown grizzly could take on a pack of German shepherds.
We would travel in a stripped down school bus. The back half would be enclosed in fencing bolted to the floor. It would contain weapons, tools, gas, food, valuables, and radio equipment. The front half would be carpeted for the dogs. The roof would have an antenna and possibly more storage space.
I would need to build some sort of reinforced scoop on the front of the bus in order to push abandoned cars out of my way. I imagine that there would be a few places that would be impassible due to the heavy traffic in the area before everyone disappeared.
Also I'd rob Fort Knox because there wouldn't be anyone to stop me.