I couldn't agree more with Brad Feld on this one - running around a city is the best way to get to know it. In fact, I make a point in every city I go to, new or not, to explore as many mornings as I can by taking a nice long run. I'm an explorer in general when travelling, but running is of course a bit quicker, and I make mental notes of places to explore more later in the day.
Interestingly, I find that I can run almost twice the distance in a new city on a trip than I can at home. The new sights, sounds, and smells somehow take away the boredom of running the same paths you've been on many times. I actually am not much of a runner, but always run when I travel.
My favorite cities to run around have been Tokyo (which is totally safe, and even more interesting if you run at 6am when all the bars are closing and the streets are filled with drunk teens), Barcelona (which you can see a bunch of different districts in one run), London (which has some great parks to run through), and San Francisco (there's nothing like a run on the entire Embarcadero in the morning).