As I recall, Sidwell did lobster lunches.
My mother attended Holton Arms, but I have no idea what any of these schools are really like today. I just know that if I were a younger person which school-age kids, I’d do anything to get them private schooling, if I couldn’t home-school.
I don’t know if the Catholic schools are still as good as they were when I was young and had friends attending them, but I would probably lean that way, despite not being Catholic; or toward some other religiously-oriented school.