There are several places to camp along Hat Creek.  This and Cave Campground are my favorites.  You have direct access to Hat Creek, which is a great palce so sit beside, and to fish if you have a mind to.

Nice sites under tall trees. Can be very hot in the summer so check your weather.  There are also swimming holes along the creek !  The group site here are pretty open while the single sites have more shade and coverage.

Sites have regular amenities, nothing special here.  Tables, food lockers and fire rings. No showers but there are showers you can rent down the road for campers.