When you say "interesting places," do you mean road- or transportation-related things to see or just interesting things in general?
Primarily road-related things (can you walk to get good pictures of I-695 or US 50 for example?)
If you want an I-695 shield, probably the best chance (and I emphasize "chance") might be to take the Metrorail Green Line to the Anacostia stop, then take the exit located closer to the rear of the train, go up to the top of the parking garage, and point your camera at the overhead signs on the highway (I do not say BGSs because as of a few weeks ago at least one of them was orange). You'd need a zoom lens to make it work. All the I-695 signs I know of, which is not many, are in a work zone on some fairly high-speed roads with no good pedestrian access. I-695 itself extends further than that but doesn't have the number posted. Also, note that a couple of the neighborhoods I-695 runs through can be a bit rough.
For a trivia point, insofar as I know there is still a sign for I-95 and I-295 to Virginia and Maryland located underneath the L'Enfant Promenade on D Street SW. The sign most likely predates the renumbering of I-95 to I-395. Down the street from there where D Street passes over the 9th Street Tunnel on the north side of the street you can find a weird "Do Not Enter" sign that is shaped like a stop sign.
Part of what makes your query tricky is that you specified places you can get to on foot. The pedestrian/bike path over the Woodrow Wilson Bridge is a nice walk or ride, but getting to it without a car or bike is a bit of a hassle. It's a long way from the nearest Metro station, and the trip BACK would seem even longer. To me, as a long-time resident of Northern Virginia, the most interesting road-related thing going on right now is the widening of the Beltway in Virginia to add high-occupancy/toll lanes, but obviously you can't easily view much of that without a car either. There's a pedestrian overpass on the W&OD Trail just north of the I-66/Beltway interchange, but it's a long walk from the closest two Metro stations. Of course, it also helps that I've seen the renderings for what they're doing and that I drive on that road at least once a week—I'm sure watching the project evolve is an important part of why I find it interesting.
I suppose one bit of DC road arcana that you could do would be to walk the notorious closed portion of Klingle Road. You'd need to take the Metrorail Red Line to Cleveland Park, then walk down Porter Street to the interchange there. Look for the fenced-off road with the "Do Not Enter" sign. Go over to that fence and slip through the gate or walk around it. Klingle Road was a public road for many years that was closed due to storm-induced erosion damage in 1991 and it's never been reopened as local residents and city officials have fought for some 20 years about whether it should be rebuilt as a road or turned into a biking/walking trail. (Lawsuits continue.) The road runs through the woods, under Connecticut Avenue, and up a hill; the other end of the closed part is blocked with jersey barriers. If you look at a map of DC you can probably figure out where the closed segment is by noting the two unconnected pieces of Klingle Road and tracing the route through the park between them. NOTE, this is not a walk you do in bad weather or at night. Don't even consider going down there at night. The pavement is uneven and broken up and there are no streetlights; there are also occasional rumors of drug activity and the like because it's so isolated, so I could understand not going at all. There is a sign saying pedestrians are prohibited, but plenty of people ignore it. Obviously, you go at your own risk.