There are campgrounds just outside the park in all directions but you are out of luck for RV-less camping. And the wilderness areas I suggested are at least a four hour drive - there is no easy route from other areas to Yosemite, you are going to be on narrow two lane roads winding in and out of the mountains to town, and then back into the mountains in another direction. Jennie Lakes is in Sequoia which is a good two hours drive from Fresno, and Yosemite's another two hours from there.
Bass Lake (south of the park) may offer you a good compromise - it's an hour from the park and very busy but I believe some of the campgrounds at least have loops for tent camping. There are two or three trails, dog friendly, Goat Mountain (4 mile one way to a fire lookout) and Willow Creek (2 - 3 miles, waterfall and swimming holes) near the lake and Lewis Creek (trailhead along 41 north of the turnoff to Bass Lake) which is an easier hike between two waterfalls. You will not find a campground in this area near a lake without noise, boats, kids, other campers, but it's the best there is within an hour of Yosemite. Seriously, Yosemite draws people from all over the world, and there really is NO quiet camping nearby in summer/early fall. You're not going to be able to disperse-camp in National Forest land in anything resembling what you describe. You will need to drive a significant distance to get privacy too.