Within a 30 minute drive:

White Sands National Monument

New Mexico Museum of Space History

Imax shows at planetarium

The Toy Train Depot

Kid's Kingdom Playground

Alamogordo Zoo

Indian Petroglyphs

Cloudcroft, a quaint "village in the sky" in the mountains

Oliver Lee State Park

50 miles of bike trails, from the desert floor into the mountains

A bit further:

Billy the Kid country, at Lincoln

Valley of Fires State Park, (lava flow)

White Mountain hiking

White Sands Missle Range Museum