Too many to list, runs the gamut from cheap (relatively) to the pricey.
The General Palmer is right next to the Depot, and the Strator is only a few blocks. They are the historic places, if you want that experience.
I have stayed several times at the Best Western Rio Grande, which is only a 3 block walk from the front door of the Depot. It is actually right beside the stubb-ends of the remaining yard tracks to the south of the Depot. Very nice, with indoor pool.
Lots & lots of choices heading up the main street to the north towards Hermosa. Eateries too.
Durango has it all.