I spent my first 50 years living outside of DC. I grew up in Maryland.
You do not want to drive in DC, traffic is pretty bad, parking can be a competitive sport.
Cherry Hill Park, in College Park MD is your best bet. Its a great place that will enhance your visit and enjoyment. Transportation options offered by Cherry Hill Park to the Metro trains are your best option for enjoying most of the Downtown area.
There are more economical RV Park options farther away (State Parks, private and KOAs) if you prefer to drive into DC from a campground farther away.
If you plan to visit a lot of the Northern VA area, you might want to move to an RV Park located in VA partway through you visit.Northern VA traffic is notoriously awful.
Be warned, it is an expensive area to explore and so worth it.
Pack a lunch and snacks if you want to save money.
Free Smithsonian Museums make up for a lot. Take advantage of them, they are outstanding.
Highly recommend you research the sites you want to see and make a "plan" of sorts. So much to see and will be much easier if you have an idea of where places are located in relation to Metro Train Stations.