Find a good stout Hammer. With the Hammer I break into whatever else I need / want. However... If there is truly no one else left, I am not sure what would be the point of carrying on / exploring. Do dogs / cats / cattle / horses survive whatever annihilates everyone?
1. Search food and medical supplies 2. Move to somewhere pleasant 3. Stay the f*** away from areas with nuclear reactors or similar stuff that fails catastrophic once humans are gone. 4. Prepare to die. Get some weapons so I can at least shoot myself before dying of some disease or radiation poisoning.
Because it is there to explore... and technically it is yours. That's actually the crux of the question. It's something that I have had many fun discussions about with friends/family. Not everyone can happily cope being alone, while others would get along fairly well even if left in isolation. I think most people wouldn't do very well. The equation can be tweaked a little by adding a few choice survivors in the scenario. For instance, it makes the situation much more pleasant if you could have 1, 2, 5 or 10 other survivors of your choosing with you. This topic was explored in the movie Bokeh. The scenario only said that humans die, so dogs, cats and cattle are still around (although pets in houses would starve/thirst to death). A bit gloomy, but fair enough. This message was sponsored by @Crowsfoot Well, you would have an unlimited supply of free paint, brushes and models.
Then you really missed out. Ocarina of Time is fantastic and is pretty much a perfect game for its time. I did play DK 64, it was fun.