I get vacation time next week, so this is my contribution.
This site gives the hotels, restaurants, etc. I don't know which will handle a large group.
http://www.cloudcroft.com/ There are email contacts for each. You can choose the hotel overlooking Burro Ave. or pick some of the cabin sites (individual cabins like back in the 50s). There are also restaurants listed in the site. I've always eaten at a restaurant that can't fit 10 people inside at the same time, so I'm not much help here.
Nearest bike shop: Champions in Roswell. There is also Barnetts of Las Cruces and Barnetts of El Paso. Champions is closed on Sunday and Monday. I don't know about Barnetts, but they have lots of good bikes to admire.
Here is some information on rides...
Cloudcroft RTE
How to get there
From the West go to Alamogordo. Take Highway 82 east to Cloudcroft. This is a nice curving road, but you might get caught behind traffic.
From the East go to Artesia. Take Highway 82 west to Cloudcroft. Cloudcroft has a gas station. Highway 82 east of Cloudcroft and Highway 244 have good curves.
While in Cloudcroft
Cloudcroft is at 8,600 ft elevation. It will be 20°F cooler than the lower flats.
MUST STOP: Cloudcroft Mercantile for pastries. OUTSTANDING PIES (order early for pick up later and take home to an SO), FRESH BREAD, croissants, and much more. Cloudcroft has some interesting shops (including antique shops) and small restaurants to explore and try.
All suggested rides are on paved roads except for the road to Sunspot. Yes, there could be deer and cattle on some of the roads. Other gravel roads lead off from the paved roads, but I don't know where any good ones are. Punch these into a GPS or Mapquest to get the miles and time.
Short East Loop
From Cloudcroft take 130 to 24. I think this is the junction that has a gas station. Pump is always “on”, so pump your gas and go inside to pay. Talk to the good people there and enjoy a pop/soda.
Take 24 to Weed and explore the store, if it is open. Probably closed on Sunday.
Take 24 from Weed to 130 to Mayhill.
Take 82 from Mayhill to Cloudcroft.
Long East Loop (gives you a flavor of the countryside, but has quite a bit of relatively straight road)
From Cloudcroft take 130 to 24. I think this junction has a gas station. Pump is always “on”, so pump your gas and go inside to pay. Talk to the good people there and enjoy a pop/soda.
Take 24 to Weed and explore the store, if it is open.
Take 24 from Weed through Dunken to 82.
Take 82 west to Cloudcroft.
Long West Loop
Take 82 west out of Cloudcroft to I-70 north (curves).
Take I-70 north to Tularosa.
Take Highway 70 east to 244.
Take 244 over the hill to Cloudcroft (curves).
OPTION: continue on Highway 70 to Ruidoso and find your own way back.
Sunspot
There is a gravel road (about 18 miles on county road 6563) that takes you to Sunspot, which is the site of the large sun telescope. Worth the ride if you can handle gravel and if it is open that day for tours.
Over the Hill (excellent ride, but absolutely no shoulders)
Cloudcroft east on 82 to 244.
Take 244 over the hill to Highway 70.
Now you can 1) return by going back over the hill, 2) turn west and follow Highway 70 back to Tularosa and home, or 3) turn east and go to Inn of the Mountain Gods Casino and to Ruidoso. There are two casinos named Inn of the Mountain Gods: one on the way to Ruidoso (the "big" one) and one in Ruidoso. Ruidoso is a resort type town with small artsy shops and great eating at local establishments. The back road from Ruidoso to the "big" casino is a fun ride as well. From the big casino you can take Highway 70 east over Apache Pass and back to Cloudcroft on 244.
Curves
For the sport bikes, get up early to avoid traffic and go east on 82 out of Cloudcroft. When you get to the bottom of the hill, turn around and come back or head west or north or where ever you want to go. See West Loops.
Joggernot