The areas are definitely safe at night. If you're getting a DCA-area hotel and rental car prices are only $40, I can see the appeal. Don't overlook the cost of overnight parking, though, unless that's included in your room rate. Personally, I find the "hassle factor" with the rental car not worthwhile in this case. Uber may be a better compromise between the rental car and Metro, especially if you're going from DCA to the hotel to drop your belongings and then heading out again. That said, if you're seeing those sights later in the evening (> 8 pm, for instance), you'll have a better chance of finding on-street parking, especially between the Lincoln Memorial and the Washington Monument and heading out on foot. Be mindful that the distance from the Lincoln Memorial to the Capitol is about 2 miles, so it's not a short walk round-trip.

Keep us posted on the details about where you're staying and when, as that information will help everyone give you the best advice about how to get around. D.C. traffic is very dependent on where you're going, the time of day, the day of the week, and the month of the year, so the answers you get might vary with more details.