I've camped in two places, it depends on how much snow they have really. There is a scenic loop right before mammoth, after the town but before the first parking area you cant miss it and you just turn off that road somewhere and find a nice flat area. The other place I've camped is right off the highway and instead of turning left to go to the town of mammoth you take a right and drive up into the hills there. Im not sure how "legal" the camping is but my buddy camped for a month two years in a row in the two different places and never got hassled.
Mammoth scenic loop
https://www.google.com/maps/place/Mammoth+Scenic+Loop/@37.6570542,-118.9927538,19z/data=!3m1!4b1!4m2!3m1!1s0x80960da21045782b:0xc27ad6c0ecfd402a
second camping area (around this pin drop)
https://www.google.com/maps/place/Old+Hwy/@37.6439887,-118.9101552,17z/data=!3m1!4b1!4m2!3m1!1s0x80960ee1112f169d:0xc52b9123329c2cce
Hope that helps. The mammoth inn isnt too expensive in the spring but I wouldn't expect to pay less than like $100 a night.