I am so sorry you're limited to just a few options! Mount Vernon has some great food, but most of the nicer places are not "American-style" cuisine tbh.

The Mount Vernon Marketplace would be a safe bet since it's a large, food-court style place.

Marie Louise Bistro if you're willing to spend some coin? The menu leans French/Mediterranean, but they still have mac & cheese, hanger steak sandwich, croque madame as just a fancy ham and cheese sandwich?

I've heard positive things about Poet's Modern Cocktails and Eats, too! Not too far of a walk from the Museum. Warning that according to reviews, the in-person menu may be different from their online menu (the parent company of the hotel has yet to change it??)

Personally, I need to go check out The Royal Blue-- a newer bar/restaurant but the menu looks great!