I’m also a single young woman in DC. I have a roommate but basically live alone, it’s definitely doable. I live around Park View/Petworth and have a decent apartment within your price range, honestly I’d recommend joining a FB group for women in DC looking for roommates or bumble BFF to find a roomie. A lot of people prefer to live in apt complexes but I have had a good experience with a smaller landlord who is chill and doesn’t mind pets. Cameras are subsidized in DC so you can feel a little more secure about that, I also have extra door alarms I’ve gotten on Amazon that work well. I also used to live in NY. Honestly I think it’s pretty comparable, but I’ve never been a victim of crime in either city. There is more catcalling here that I’ve experienced, but that could just be my area. If you have any other questions lmk, hope this helps!