Ah... the South West. It'll always be in my heart, the most magical place I've been to in the US.
As well as having some great trails to mt. bike and not so bad roads to road ride.
The 100 mile loop I believe jppe refers to is usually the 85 mile "Enchanted Circle" ride (plus extensions) that goes either clockwise or reverse, up to Red River and Eagle Nest Lake, over 2 passes. CW is considered somewhat easier due to the straight downhill to Taos off Palo Flechado Pass. Never done it, but it's popular on the Pedal the Peaks tour.
Canyon de Chelly (pronounced "Shay") is all Navaho Rez. lands and is pretty good riding, just hot at noon in July.
And to Rob, a correction that Santa Rosa is east of ABQ and does indeed have the famous diving spot Blue Hole. There's another down near Roswell/Artesia somewhere.
And, yes, there's a lot of mt. biking out in the desert, mostly as there's so much open space with no paved roads. The road rides have to be carefully planned to have locations that have water on the route.
Going back someday
SB