I would want to go waaaay back and see what the first real "advanced" civilization really was. Was it Atlantis? Was it Eden? Where is the real beginning of "us" as an aware and thriving community? And, since you've given me a whole day to travel around, I then want to stop by and see what prompted the Veda's to be written. The stories of UFO's and weapons from the sky fascinate me. Towards evening, I want to see Ezekiel's Wheel and Moses' burning bush. A brief stop by Egypt and the building of the Sphynx would be great as a little fly-by as well.
Even tho I have a real fear of heights, I'd get in that car and take the tour! I have a secret love of speed...the faster the car the better! Terrifying but, man, what an adrenaline rush! (LOL Now you all know my secret vice!)