We heartily recommend Leasburg State Park about half an hour north of Las Cruces, NM.
They have a sort of town hall meeting area near the visitors' center which has beautiful shade trees, cactus, green grass and covered picnic tables and grills.
We spent Memorial Day weekend there, and on Saturday night, they had a show called Meteors and Music. A local folk band played, and the local astronomy club came out. The park has an observatory, and everyone got to look at the planets.
One of the park rangers is part-Navajo and he told stories to the kids. It was great.
As for facilities, the park has a great bathhouse,and covered and shaded campsites, and is just a short hike from the river. We fished, birded, and saw wildlife, including horned toads.
No fire ban, so we made a campfire at our site, and the kids roasted hotdogs and smores.
Not bad for $14 a night for tent camping.