OP, don't worry: D.C. is fine. Better than fine--I know what the city was like 20 and 15 years ago, and its current state of my city represents a phenomenal improvement. It is nowhere near Mexico City.

Metro hours can be iffy on weekends, but it's a manageable risk: check the schedule and the next-train estimates on wmata.com on your phone and at least you won't be surprised. On weekdays, you can still wind up 5 minutes late, but you have a much better chance of showing up on-time if you take the train than if you hop into a car.

Another good option for getting around car-free: Capital Bikeshare. $7 gets you a day pass that's good for free rides of up to 30 minutes between stations.

And don't forget your own two feet. The District is a thoroughly walkable city... although walking faster than 3 mph on a humid afternoon in August isn't recommended.