Depends on your budget. You might want to look in Arlington, near the Rosslyn or Courthouse metros (those would be the closest besides Foggy Bottom). In DC, I just found a townhouse near L'Enfant Plaza (10 minute metro ride to FB) that is reasonable, so maybe you could try there.
Try some realtor's websites, I've been using
Long & Foster Real Estate, which seems to have a lot.
McEnearney - Northern Virginia, Washington DC, and Maryland Real Estate Services is also good. Btw, another townhouse in the community I mentioned is listed as #DC6673234 in Long&Foster. Doesn't mention dogs, but it's worth asking.