Parking is going to be a major pain no matter what. If you're willing to spend $40 for a rental car, spend less and take an Uber, depending on how close/far your hotel is from a Metro stop. Seeing the various things you want to see will still involve a bunch of walking, as it doesn't make a lot of sense to drive among them. Map out a route before you go that will let you walk without backtracking, then take a car/Metro to one end and leave from the other.

As to safety, there will not be an issue. That whole area is probably the best-surveilled neighborhood on Earth.