If a person moves to a different town, but still has the same comp, will a website owner beable to tell?

Actually if you move to a new town, you should get a new IP Address. Your IP Address is igned via DHCP by your ISP (unless you pay extra for a static IP). So for instance if you have comcast, your IP address will be igned by them. It doesn't follow your computer around. The only other thing they may be able to see are cookies stored on your computer. Be sure to delete all of the cookies, and you should be all set.