Eventually you need to wend your way south to the Sacramento Mountains. The Tularosa Basin/ White Sands sit at around 4000' MSL, while the Sacs rise to the mid-9000s, with Sierra Blanca outside of Ruidoso topping out above 12k. LOTS of twisties and 2ndary roads here.
The ADVrider site has a thread about some of the more scenic rides in the state. Watch for free-roaming horses on reservation lands, and piles of horse hockey in the middle of the road on those early morning rides. Route 66 is mostly I-40 now but still some awesome ridng out that way. Be sure to check out the Land of Fire and Ice to the west of ABQ when the weather's cool, and tours of the Trinity site down this way when the cuffs come off the country.
Take your old Beemer out at the Balloon Fest, drop hints about being a sport pilot, and I'm sure someone will offer you a ride in one of those things. Welcome to the state!