Another vote for Meadowbrook, it is a long-time lesson program but as others have said it can be far from where you live depending on where you are in the city, and they only do programs, not drop ins (summer you can do 4 lesson packs but throughout the rest of the year you have to do a set weekly lesson for 32 weeks and it is not cheap).
I agree that PG CO could be a good bet depending on where you are in DC. Also look at Northern VA in the McLean/fairfax area. Rokeby is very close to dc but not sure what lesson horses they have - worth a call! You might also want to give Clairvaux, Jonelle Mullen, and/or Cavallo farm a call - all in Va but within an hour drive of the city, I’d venture a guess. Hope you find a great option!