I'm only about 4 inches taller than you and I live here!! Honestly, DC is a very safe city, I never feel at all threatened walking around by myself, even at night. Over the summer we'd take a walk every night before my daughter went to bed and even on nights that my husband was on call I'd go myself without a problem, and it was generally dark when I'd go. Really, the bad parts of DC are not where you'd be going cause there are no touristy things there (like SE DC) so you really don't need to worry about safety any more than you would in LI (and I say that coming from NJ, in a very small, safe NYC suburb).