I have the perfect place for you--Elephant Butte State Park's Monticello South Campground. It has widely spaced, long sites with 30/50A electric and water at each, an on-site dump, a new restroom/shower building, paved roads, a boat ramp, and no stores or houses anywhere in sight. It is located 10 easy, paved miles off I-25, so has absolutely no traffic noise. The only downside is no trees, but that shouldn't be a problem in October and each picnic table has a canopy.
Just as one example, Site #17 is 41 x 91 ft (!), with a gravel and dirt, 41 x 35 ft pad. It backs up to the lake, but the campground is on a hill several hundred feet above the lake. And New Mexico has the lowest-priced State Park campgrounds in the nation--$14/night for electric sites, which includes the park entrance fee. You just can't beat it along that part of I-25!
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