Recently, on a visit to Lille and Paris, France, I did a couple runs with, for the first time, a camera (in a plastic bag to keep the sweat away) in my hand, which did detract a bit from the runs but compensated with photographs of sights without the tourist crowds. Here are some examples:
Lille: The narrow cobblestone street where I was standing and taking this photograph curved around to my right. From the map, I knew, as I was running around the curve, that this Cathédrale Notre-Dame de la Treille was coming up. The gradual revealing of the cathedral, the transition from the narrow street to the open square, in the serenity of the early morning, was quite something--regardless of whether one goes to church or not.
Lille: Créperie de la Vieille Bourse (best dinner of the trip!) at night (left) and morning (right), immediately after the street sweeper truck had passed by.
Paris: An 8-mile run that covered the Tour Eiffel, Arc de Triomphe, Avenue des Champs-Elysees, Grand Palais, Hotel des Invalides, Jardin des Tuileries, La Rive Gauche, and more. Here's a crowd-less Tour Eiffel.
Have map (and camera) - Will travel!