You didn't give a geographical preference, and if you really are in Cleveland Park, you may not consider Rockville too far. There is a place midway between the Beltway and the city of Rockville called El Patio. It is Argentinian, and the empanadas are of the flaky dough variety - very, very good. Excellen quality fillings, really delicious.
It is a little bit difficult to find. Turn right on Twinbrook Parkway, and it is almost on your immediate right. If you know where Urban Barbecue is, it is on the other side of that parking lot.
You might want to try la Choza. They have fried empanadas. There is a restaurant in Falls Church and also a stand in the Ballston Food Court. It is Ecuadorian, I believe, but that will not be evident at the Ballston location, with a much smaller menu. I think the empanadas are only ok, but YMMV.
Then you could always try a Colombian restaurant, such as Monserrat in Arlington or Brasa Roja in Fairfax.
If I'm correct, a Columbian empanada is very similar to a saltena. If you're in the Alexandria neighborhood of Arlandria (little Chirilagua) you can find excellent saltenas at My Bakery and Cafe, and Marcell's Bakery. Both on Mt. Vernon Ave.
Marcella's also sells beef and chicken saltenas at a table at the Del Ray Farmers Market on Sat. mornings.