There used to be a Budget rent a car location at the Ramada Inn downtown, also an Enterprise location. Rentals may be cheaper in Grand Junction, but that's also a drive back.
If you do an overnight, Hotel Denver is located immediately next to the Amtrak Station, just across the street. It's an older property but rates high on Trip Advisor ratings. The Hotel Colorado is located behind the hot springs pool, has lots of history, but the rooms are older. Hot Springs Lodge is owned by the same company that owns the pool, and you can get discounts on pool visits. There's also a number of newer properties, including both the Holiday Inn Express and Hampton, both located downtown.
There was a very nice bookstore downtown called the Book Train that had a great magazine assortment, also decent book selection for a smaller independent shop. Hope like heck it's still there. The Glenwood Springs Vapor caves is a great place for a massage, also steam caves.
If you do some traveling, definitely would recommend a trip to Redstone / Marble area. This is where the Marble for the Lincoln Monument came from; the drive is very scenic, and the river has chunks of Marble that were tossed there from the narrow gauge railroad that used to run between Carbondale and Marble. Redstone is the home of a historic hotel that was built by a steel company I believe when they had mining operations in Redstone.
If you are into railroad history, there is a lot to see in the area. In addition to the Rio Grande railroad, the Colorado Midland Railroad also provided service to the area. Their old right of way is where the train currently runs in Red Canyon west of Glenwood; the original D&RG route was on the side of the canyon where the interstate is. The CM right of way continues west from the river bridge on the far side of the river to New Castle, where it joined the D&RG. Old bridge abutments are still visible in the river in New Castle. There was also the railroad to Marble, noted earlier.
Have a great trip, it's a neat area -