I know the answer to this one!
Trailer your bike to the Denver area

then up through Rocky Mountain National park. From there, take 40 down to I70. I70 west to 91, south on 91 through Climax to 24. Take 24 south, with a spur trip to Independence Pass. Continue down 24 to Poncha Springs, where you get on 50 west through Gunnison. Just past Gunnison, get on 149 south. This takes you over Slumgullion Pass and past the headwaters of the Rio Grande. Continue to South Fork, where you get on 160 south. That takes you over Wolf Creek Pass. In Pagosa Springs, get on 84 south. 84 will take you to Chama, where you'll make a right and stay on 84 to Tierra Amarilla. There, you'll make a left onto 64, which will take you past the Brazos cliffs and on to Taos. You'll cross the Taos Gorge bridge just before entering town. Shoot straight through Taos, and you'll end up on rt. 68, which follows the Rio Grande through a gorge. There's also a mountain route you could take, but it's a lot more complicated. When you get to Espanola, be careful.

On the south side of town, take route 30 to route 502. A couple of miles later, take route 4 past Bandelier National Monument. Route 4 will take you over the Jemez mountains to route 550. Make a left on 550, and that will take you to I25 just outside Albuquerque.
From Albuquerque, you can take the faster route, which is I40 to route 117, which you then take south to 36. South on 36 to route 60.
The longer route is interesting if you've never seen the Very Large Array. Take I25 south to route 60, which goes right through the VLA. Either way, 60 will take you through Salt River Canyon all the way to Phoenix. Another choice would be to cut south in Springerville on 191. Take 191 to 70, then meet up with 60 again a little east of Phoenix.
If swinging north a bit after hitting central Kansas takes too long, head for Colorado Springs and take 24 to 285, which brings you to route 50. Take 50 west to Gunnison, which brings us back to the route outlined above.
I haven't mentioned which are particularly good roads, because listing the duller roads would take far less time.
When will you do this?