Travel the world collecting as much artifacts of Earth's history, to let any future alien life-forms that travel to Earth can learn the history of Earth and its dominant species, humans.
Proceed to research for a way to somehow create a baby, despite being the only human left. Maybe attempt create an artificial breeder to pass on my genes/human race. It will use eggs found in one of those weird egg-storage-facility things. In the case of infertility from old age, I would use semen from sperm banks to impregnate the artificial breeder.