Two summers ago, we had a family camping trip near Mt. St. Helens, and it was fabulous!! I'm trying to remember where it was and am coming up blank, though :( We were not actually at Mt. St. Helens, but close enough to easily get there and visit. We had a great camp ground with flush toilets (I believe - we had little ones, so don't remember dealing with pit toilets with them), the camp site was spacious and great for the kids to ride their bikes around, and we were close to some great hiking. We must have been on Mt. Ranier, because we drove up to the visitors center one day. The scenery was breathtaking, and I'm sure there was fishing around, though none in my family are fishers.
Ok, looked it up since it was driving me crazy! We camped at Ohanapecosh campground - I think it's near White River. We live in Oregon, so the drive was very reasonable (maybe 3 hours) and again, very convenient to Mt. St. Helens. You will need to make reservations for the campground I named, but if you google "camping at Mt. Ranier" you can find info about it and the other 2 campgrounds in the park. We were there for a 3 day weekend and had a glorious time!
On the Washington coast, we've camped at Ft. Flagler (which is Whidbey Island) and near Westport. Both have some great camping. I haven't been up there in a while, so am not very good about details there.