We have stayed a few times at Silver Springs and its one of our all time favorite . Recently stayed at site 13 and almost no one else was nearby.
Most of the sites are larger than average and mostly separated from the other sites.
There are two main loops (both close to the highway) and one dead-end loop on the southern side really close to the river.
The close access to several hiking trailheads, the White River itself, Goat Falls trailhead (almost no parking there), Crystal Mtn Ski Resort (open in the summer for Gondola rides to the top of the ridge with amazing 360 degree views and a restaurant (check for last seating times)), Sunrise Mt. Rainier entrance, and the rest of Chinook Pass, and close drives to Enumclaw, makes this a fantastic no service campground (public bathrooms with sinks on each loop).
There is a slightly hidden trail through the middle of the northern loop that we accidentally discovered this trip - it has a large group campfire / picnic area that would is not for camping but for day/evening use for a larger group with several picnic tables and cooking spots with a nice short and beautiful walk along the small creek inside the camp loop.