Sandra,
Reserve Airport is supposed to be getting a pilots/visitors lounge soon, likely within 6 months. It is funded and just waiting on the county to start the site preparation work.
I am better able to speak to dirt/gravel/ turf airstrips than I am on paved runways. A real favorite is Negrito Airstrip(0NM7). It is 18 miles SE of Reserve.
It had a vault toilet placed there last year. NMPA is having a work party there 1st weekend of October to pour a concrete stoop and access ramp for the toilet. I have been personally cleaning it, but last time was mid August, and there have likely been hunters there. It will be cleaned again before, during and after the work party. There is no running water there. We always recommend no wheel pants for any backcountry airstrip, but Negrito is normally very smooth for dirt/gravel/turf runway(s). Many folks land with wheel pants. Since it is owned by USFS, a phone call is required before going. It is high elevation at 8143', but a 182 can do well on the 7500' runway. There are tie-down anchors(ropes required) on both sides of the main runway at the camping area. East side is better. There is also a fire ring.
Another beautiful place is Me-Own Airstrip(1NM0). It also has a vault toilet that USFS maintains, but the toilet has been closed for COVID, and I don't know the reopening date. It is lower elevation, but a shorter runway and still good for a 182. It is also normally smooth, but will have some tall grass beyond the center 15' until I mow it again in late October.
Lots of info is available for both of these on the NMPA website under backcountry/safety briefings.
www.nmpilots.org
and on
www.Airfield.Guide
As for mountain paved airports, maybe Sierra Blanca near Ruidoso allows camping. Also Angel Fire might allow camping.
Hope this helps.
Ron Keller
NMPA Backcountry Co-Chair