If you are looking for under 500k, Petworth is a terrific option. There are a lot of dogs in the neighborhood (my wife and I LOVE our two beagles!) and there are pocket parks (small areas at the intersection of diagonal and straight streets) as well as the big parks in the middle of Sherman and Grant circles where lots of people with dogs congregate. For $500k (or certainly less) you will be able to buy a full rowhouse, and get ~2000 sq feet and a small yard. 495 is only about 10-15 minutes away via New Hampshire Ave, and there is tons of new development coming into the area, and new restaurants are opening up with some regularity at this point. In addition, you will be between 20-30 minutes from downtown (depending on walking distance) and can get to Verizon Center and Nationals Park in that same amount of time.
You will definitely be able to find plenty of places that could use a little love. Good luck with your search!