The first thing that comes to mind is....
I happen to be a big fan of scavenger hunts because they are fun and free. And what better way for your out-of-town guests to get to know your city?
I would split people into teams of four or five. You could do a Random Acts of Kindness Scavenger Hunt, but I would probably do a regular digital camera scavenger hunt if I were in your position. People are already going to be a little out of their element, and I wouldn't want to make them too uncomfortable.
I would put easy things on the scavenger hunt like: "Get a group picture in front of a statue," as well as wacky things like: "Take a picture of a group member wearing a wet suit and doing a headstand." Well, I take it back. I think I would look at the guest list and figure out who would be going on the scavenger hunt. Then I would tailor the wackiness level to the group. You could do a perfectly sedate scavenger hunt that involves visiting historic or unique things in your city.
I like to assign point values to different items, just to add a little competitiveness into the mix. I would give people a good chunk of time to complete as many items as possible and then require them to return to a centralized place by a certain time. I would make one of my friends the Scavenger Hunt Judge who would flip through the photos and certify points. I would give the winners a cheesy prize.
So that's how I would solve your conundrum, but I'm eager to hear what others have to say!
P.S. You might also want to check out this List O' Fun Things to Do at a Wedding.