Carol,
My wife and I visited Alamogordo the first part of November. We stayed at the FAMCAMP on Holloman AFB. Since the AF is footing the bill for you, you may considere staying there. We paid $14 a night with full hook-up including cable and covered patio. The laundry is close by and a lot cheaper than most RV parks. Plus we shopped at the commissary and base exchange.
Lots of great places to visit. Such as, White Sands National Monument, Ruidoso (and Ruidoso Downs), and Cloudcroft. This is a great time of the year to visit there. The weather is fantastic. Summer time gets a tad warm for me (120 degrees).
Good luck on your trip.
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