Your best bet would be Albuquerque. Several Motel 6 properties here. You would enjoy Old Town, it is over 300 years old, lots of shops and good restaurants.
I-40 to I-25 to US 550 to Durango is thie quickest route.
You could stay over in Santa Fe, then take US285-84 to Pagosa Springs, and US 160 from there to Durango. A little longer route, but really pretty scenery.
This is tough because of the competing things you're looking for. As noted above, Albuquerque is much the best intermediate stop for a Motel 6. However, from there you have a choice between a dull drive that's (barely) within your 2-3 hour range ((US 550) or a much more interesting one that isn't (I-25 to US 84 to US 160). The latter route has all kinds of entertaining breaks in the driving, which 550 does not, but there's no getting around the fact that your second day would be longer, even if you overnight in Santa Fe instead (recommended if you choose that route). What's your priority here, short distance from Durango or interesting side trips and things to do en route? Decide that before deciding which route to use.