If you find yourself in the DC area you need not forgo your ritual run. In fact, you can best see the city by running! After you get past the initial “oh I want to run on the mall!” phase (and you will get over that about 5 minutes in) try a route that takes you through the Smithsonian Zoo. That’s right: You can run through the zoo and lots of people do!
The zoo is free, open to the public by 9am (earlier I think during the summer), and has wide pathways that cut straight through (it’s uphill if you come in off Rock Creek, downhill if you come in from Connecticut Ave) and in the early morning and winter it’s empty except for the animals and other runners. You can bypass Rock Creek Park by just heading back uphill along Harvard.
Don’t run through Rock Creek if it’s dark out, but the zoo grounds are pretty (especially with fall foliage in Rock Creek Park), and it’s great seeing the animals. Be on the lookout for Pandas, big cats, zebras, and great apes and thankful that you aren’t stuck in a cage like they are.