El Paso's Keystone Heritage Park and Botanical Gardens is a surprising place. In the middle of the city, the park sits in the shadow of the Franklin Mountains. Its wetlands provide the visitor with excellent birding opportunities, and the garden is simply lovely for a stroll.
You can read more about it here and here.
For a list of other nature centers in the region, click here.
Keystone is a great place for birdwatching. For information on birdwatching within the Texas Mountain Trail region, visit: www.texasmountaintrail.com/bird