There are parking garages in the side streets, we parked it without any problems, the price had to be fairly normal because I don't remember it
On the main park there are parking spaces.
Parking in DC is a hassle. You might get a 30mins or more somewhere along the road away from the park but I wouldn't bet on it. Avoid the one-ways which can be confusing. Find a paid parking lot and walk or bike.
In the neighborhood
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