On the West end of the Mall – [I personally prefer the West end to the East end]
The Vietnam Memorial always makes an impression on me. It is very personal to many. Others like the fairly new WW II Memorial.
The Lincoln Memorial and Washington Monuments are at opposite ends of the reflecting pond. If you are going in mid-October you should get some Autumn color. I’ll also note that there are 2,700 Elm trees on DC parkland, primarily on the Mall. So the Autumn color is from what has become an unusual and endangered tree since the Dutch Elm Disease.
The Jefferson Memorial is just across the tidal basin and provides a good photo. Typically you see this in the Spring during the cherry blossom season.
If you wander just a bit off the mall, the White House and the Old Executive Office Building are in walking distance up 17th street.
At the opposite end you have the Capital building and nearby Union Station (if you care for indoor architectural photos). There is also the Botanical Gardens (if you care for indoor botanical photos).
There was a time when the Park Police gave photographers problems, especially following 9/11. That’s mostly past. You can still run afoul if you set-up a tripod on a walk path, stairs, or other paved area where people walk.
If you are traveling outside the city, Mather Gorge/Great Falls is a wonderful landscape area that’s worth the short drive. It’s about 30 minutes driving from the Mall (non rush – double or triple that during rush) and West of DC.