Overnight stay near Silver Spring MD

Depends on how close to Silver Spring you want to be. There are a couple nice MD state parks in the Frederick area, Gambrill and Cunningham Falls. They would be in the range of an hour plus away (unless you go during commute hours which could take much much longer). They are at a bit of a higher elevation on a ridge so could offer more comfortable camping weather. Cunningham falls is the farther of the two but is interesting because it's co-located with Catoctin Mountain national park where Camp David is.