Glenwood Springs is my personal favorite location along that route. Winter is a wonderful time to visit as the mix of cold weather and a hot outdoor pool makes for a really neat experience. Several of the hotels offer vans that will pick you up at the station, while another (Hotel Denver) is right behind the depot.
Of the the hotels, Hotel Denver grabs the prize of being closest to the depot, basically a flight of stairs and cross the street to the front door. Across the river, there's the Hotel Colorado and the Hot Springs Lodge. Both are located behind the pool.
One of the nicer places in my mind is
The Hot Springs Lodge. The lodge is owned by the same folks that own the pool, and I believe you can get discounts on pool admissions by staying here. The property is newer, maybe 20 years old, but very well maintained.
The Hotel Colorado is the main historic property downtown, although it can be a bit rustic to say the least. The public spaces are very nice, and they have a great Sunday Brunch. Guest rooms run from funky old to nice, depending on what level of room you book. In the old days, the Hotel Colorado was linked to the pool under common ownership, and Teddy Roosevelt stayed here on a hunting trip to Colorado.
There are multiple other properties including chain and local properties that you may also consider. Besides the pool, there are several nice spas (the pool has one, there's also the Glenwood Springs Vapor Caves that has underground caves that are warm and humid), and a nice downtown (be sure to check out the Book Train, a nice downtown book store that has a great magazine selection). All of downtown is pedestrian friendly. In warmer months, there is a solid surface walking / biking trail along the Colorado River east of town through Glenwood Canyon that is something you might enjoy. There's also another cave site, accessible by gondola rides downtown that I haven't tried.
If you decide to rent a car, there's multiple attractions nearby. Aspen is a short drive from Glenwood, and the town of Marble is a neat area also. There's lots of railroad history in the area, if you're into that sort of thing. At one time Glenwood was served by two railroads - Denver and Rio Grande, and the Midland Railroad. The Midland went out after WWI. The current railroad alignment occupies the old Midland roadbed west of Glenwood through the Red Canyon until it crosses over the Colorado.
Hopefully haven't overwhelmed you with info, but I do think you'd love this as a quiet stop along your trip. Have fun, let us know how it went if you get a moment -