I live adjacent to Elephant Butte State Park and am able to visit as often as I like. The lake formed by the damming of the Rio Grande river is New Mexico's largest. The most popular activities at the lake are boating, fishing and camping. I enjoy visiting some of the more secluded spots like a park near the Dam Site and my favorite is the Paseo del Rio Trail. There are lots of beautiful vegetation, butterflies and birds.
There are activities scheduled at the park throughout the year. My favorite is the Ballon Regatta (Hot air balloons). I also have enjoyed the Fireworks in July. There are also educational brown bag lunch events held monthly. You can learn about the plants and wildlife and even astronomy. My favorite time to visit is when it seems I am the only person there. Surprisingly that is more often than you would think.