Finding a good public campground within a short drive of any major city is usually a challenge. In Albuquerque, there is a great option in the town-managed campground next to the Coronado State Historical Site.
Coronado Campground has great options for both RV campers and tent campers. In the RV section, all of the sites have water and electric hookups, shaded picnic tables, and nearby restrooms and showers. The tent camping area has a large group area, walk-in tents sites, and a few developed sites, many with awesome views of the Rio Grande and the Sandia Mountains. Reservations are available by phone only and are recommended for this popular campground.
Walking distance from the campground, the Coronado historical site is well-worth an hour or two of exploration. Other major outdoor attractions within a half-hour drive include the Sandia Peak Tram and the outstanding Petroglyph National Monument.