Cleawox, Munsel and Big Creek Reservoir #2 will be your best bets on the coast in June if you want to keep fish. They're all heavily stocked with trout and hold up well through June most years. The last stocking of the season on that part of the coast just happened this past week. In late June it'll be a little slower, but there will still be fish around. Most of these lakes get both legal (8-10 inch) and trophy (14-17 inch) rainbow trout. A few have wild cutthroat as well, which should be released if caught.
If you want to fish the creeks, most all of them in that area hold populations of small coastal cutthroat. They're wild fish so most of these streams are managed for catch and release. I'm sure Rock Creek right there through the campground has fish in it, though most will probably be in the 4-8 inch range.