Adjacent Bandelier National Monument has more scenery, hiking trails, etc., and is more fully developed to support the casual visitor. Although the parks share a boundary, the Bandelier main entrance and visitor center are about 25 miles away from Valle Grande along NM SR 4.
Los Alamos is nearby, with some in-town activities it's a small town but has more than its share of ammenities and more hiking, including many trails affected by the 2000 forest fire, alas, but since then substantially repaired. These trails include some that reach the rim of the Valles Caldera and have nice views of Valle Grande and Redondo Peak. Other interesting areas in the Jemez Mountains include Jemez Springs, with an interesting archaeological site and accessible hot springs, and a number of developed campgrounds in Santa Fe National Forest, some with access to trails and fishing holes. About 45 minutes away is Fenton Lake State Park. (http://www.publiclands.or...)
Santa Fe is one of the world's great travel destinations and is about 60 miles away by road.