What campground(s) do you guys recommend? I'm asking in March because I'm sure we'll need to reserve a spot for this summer asap.
Last I looked, Upper and Lower Pines are the classics. Good luck on getting reservations. If you like the hassle, maybe camp 4. I stayed there once, and no one much bothered me. In mid-summer, it will be campground hell, with hundreds of campers, some looking for trouble. I had a reserved spot taken from me, I had used my car then to get about, and when I came back, five guys in a van parked there and took my spot. At night, so no rangers to complain to. Nowadays, they'll possibly have guns.
Tuolumne is a cooler place, at almost 8,700' elevation the people are much nicer. I gave up on car camping in the park during summer. Backpacking was much cooler and pretty reliable. No big problem there finding a spot!