Good question...
First of all, since the description is: "If you knew today was your last day on Earth, how would you spend it, and why?", It could mean that I'm going somewhere else, such as a New Earth or something :P In which case I would probably be packing my luggage and stuff :P
But if it's the end of the world...Why is it the end of the world? If there was a way to stop it I'd probably spend all my time doing that, or making something that can postpone it :P If nothing can be done to stop it, then I'd probably spend some of my day telling everybody around me how much I appreciate them, then spending some time with my friends and family, and then spending the last few hours of my life with my girlfriend <3