If you must go off the beaten...
If you must go off the beaten path the thing I would recommend would be the dry salt lake South of Clovis, but East of Portales. It's near Arch, NM closest to the Texas border. It's a big dried up salt lake. If you find a road out to the lake, you can dig in the dirt and find some really great salt crystals. I know it's a bit of a stretch, but hey, your trying to find things to do in Clovis, NM.
Another place to check out would be the Oasis State Park. It's south of Clovis near Cannon Airforce Base, it's a 3 acre lake which they stock with trout in the winter and catfish in the summer. The best thing to do there is bird watch. They have a lot of great trails and you can run into bobwhite, american kestrals, and blue jays. It really depends on the season.


Blackwater Draw