Sevilleta (“Little Seville”) National Wildlife Refuge is mostly closed to everyone but critters and researchers. The refuge headquarters does feature a series of loop trails that make for pleasant desert rambles when it’s not hot or windy. The trails are between about 4850 and 5050 feet, are clearly marked, have great views from the high points, and even have benches to rest on. Your loop walk can be as short as a quarter-mile and as long as roughly five miles.
The NWR headquarters is 50 miles south of Albuquerque. Leave I-25 at Exit 169, then make a sharp right turn to head to the HQ. The visitor center is open Monday–Saturday. On Sundays you can park at the gate, walk the quarter-mile to the visitor center, and pick up a trail guide just outside the front door. I’ll assume you’re interested in getting in a proper ramble, and will suggest a specific route. Head south from the visitor center on the Nature Loop, then turn off on the Ladrones Vista Trail and head more or less west. The trail climbs the local mesa edge, then turns north to follow that edge.
At 34 deg. 21.300 min. N, 106 deg. 53.613 min. W, you reach the intersection of the Ladrones Vista Trail and the Mesa View Trail. If you want a roughly four mile walk, turn right and head down the mesa edge, continuing east and south until you return to the visitor center. (For someone not used to backcountry trails, the descent might seem a bit scary, but there are steps in the worst spots.) If you want to add a mile or so to your outing, head north on the Mesa View Trail. In roughly half a mile, the trail turns east to drop off the mesa, then continues south and then southeast until you’re back at the visitor center. If you pick up a copy of the trail map at the visitor center, all of this will make more sense.