Following are 25 cities off the top of my head, some big tourist spots and others less so. I'm aware the list reflects my own biases and leaves out big chunks of the world and dozens of extraordinary cities, but I had to cut the list off somewhere.
YOU GET 10 VOTES! So of these 25 cities, please vote for up to 10 that you'd love to visit for a week only. You would be confined to the town and immediate environs, so you'd want to spend your time intensively getting to know the place a bit, and not drive off somewhere else that happens to be nearby.
Also, assume there would be be no jet lag, travel would be instantaneous, and visas or any bureaucratic nonsense would be nonexistent or taken care of for you. The idea is just to build up a picture of which parts of the world people think are interesting enough to visit.
The poll will not let you exceed 10 choices. Your choices are all equal; you are not ranking your chosen cities. And you may write in your OWN choice if you so desire, at the very bottom. And yes, I'm aware of the graphical glitch in the poll's header - I'm trying to fix it...