Hyde Memorial State Park, like many NM state parks, is more campground than park. There are additional campsites, some with 3 walled shelters at the park, so you're not limited to this particular campground, whose only real advantage is an illegal trailhead to the city reservoir, left by firefighters a couple of decades ago (look for a trail near the top off the campground loop hike).
It's illegal to go to the reservoir, but enough folks do it to keep the use trail well trodden. It's doubtful you'd be cited, but possible.
Personally I'm allergic to paying for camping if I can and still sore about paying $70 a night in Big Sur a decade ago when everything but a private campground was fully booked. So here's my cheap advice:
Drive another 6 miles to Big Tesuque, a free Forest Service campground with picnic tables, vault toilets, fire rings and a stream for water and enjoy the freedom from fees. If Big Tesuque is packed, drive up to the Ski Basin at the top and camp there, it never fills up for some reason, and also has picnic tables, vault toilets and fire rings.
There's also a dirt USFS road off the north side of Artist Road just above Hyde Park and a trailhead at the eastern edge of the stat epark that leads to the stream: this means shelpping your stuff a couple of miles though, downhill on the way in.
Point is, you can pay for camping here, but you need not if your prefer holding onto your cash, by driving just a few miles further.