It's been about ten or more years, but I remember we came into Durango from the north, and it's probably Rte 550 ... and it gave me white-knuckles and I don't usually get bothered by that stuff ... but a great drive and I'd do it again.
It could have been another route, but I don't see any other route on the maps. Hopefully someone else will chime in -- but do take a careful look if steep downside canyons bother you. Because if we did take Rte 550, it's pretty nasty in one long section as I recall.
If you can do a half-hour with passenger "eyes closed" the rest is beautiful. And, as I recall, the north route is on the up-side of the road, not the drop-off side, which is a bit easier to take.
