... I live in the DC area dog thefts happen a lot and I want to make sure my Harley comes home to me.
Me too; I live in DC and have two toy poodles. Generally, areas where you see others walking expensive friendly dogs are safe.
Early mornings are better than evenings. Areas I use are Sunday's for free parking and walks along the Nations Capitol, Botanic Gardens, the National Mall, and Yards Park next to the Navy Yard in SW.
If you live in the northern most part of DC near Silver Spring, there's a very nice park off Rt 410 with horses (Meadowbrook Stables) and recreation called Candy Cane City. I'm not inclined to use the Rock Creek trails if alone on the DC side; it's generally safe, but there have been occasional rapes and homicides there going back over 40 years.
If you want a nice walking or hiking area, try Great Falls Park on the MD or VA side, just beautiful! And enough people use it that you feel safe. It's a quick drive from DC.
I think of DC as a patchwork of mini-cities within a city, and every neighborhood has a distinct feel to it. It's the kind of place where you can live on a nice street, but two blocks over is wretched.
Google "best places to walk your dog in dc" for ideas. It's also not a bad idea to carry a stick or pepper spray to repel aggressive dogs.