Avoid, if at all possible, eating in a random downtown restaurant. This is especially true for the National Mall, but also near large hotels — Woodley Park with nearby Omni Shoreham and the Marriott comes to mind. There is a line of restaurants there which sound suspiciously like some other, more well known DC establishments: Mayahuel for Oyamel, District Kitchen for District Commons, that kind of thing.
There is good food to be had, for sure, but it is still overpriced.
The best food at any price is outside of the beltway, usually in strip malls.
Yes, sometimes you need to pay for the “good” attractions, but not in DC! The best stuff is free and unless you want to go to a specific gallery or museum (The Phillips collection is worth visiting) you can easily spend a week just going through the Smithsonian museums and free parks.
Two favorites that you do have to pay for: the Hillwood estate, which was Marjorie Merriweather-Post’s home and now an exhibit of (mostly pre-revolutionary Russian, including Faberge eggs) art with a small-ish but beautiful garden; and the Dumbarton Oaks museum and garden, which is so large that is bordering on unseemly considering its Georgetown location.
But the best — and free — experience would be just to walk around areas that aren’t the Mall, around Dupont and Logan Circles on a spring afternoon when trees are in blossom, or down U Street/Shaw on a Friday evening, both unforgettable experiences in their own ways.