To start with, I need to admit that I haven't had the money to take a long trip since 2010 so whatever I say is somewhat dated. Secondly, most of my trips to CO and NM over the last 30 years have been while coming back from visiting relatives in Iowa and I tend, unless somebody is dying, to take the train so I'm not in position to give much advice on airports.
I have gotten off the train(Amtrak) and rented a car at Denver, Grand Jct and Albuquerque, turned in cars and gotten back on the train at GJT & ALB. Each has points in it's favor, depending on what you wish to see and how willing you are to get off the main roads. My personal preference is to get both on and off at GJT and do a loop of some kind, exactly where depending on what I plan to do/see/explore. Sometimes it has been the "narrow gauge circle" or some close approximation of it, sometimes I've wandered into Utah, always I plan short-mileage days with lots of stops enroute. A note on motels: I am easy to please on this front as I only require clean, decent bed, & (inside) access to a bathroom with running water. And yes, I have stayed at some where the bath was down the hall. I'm also a big fan of public transit, where available, so I'm including a few notes on that.
A few specifics:
Denver. Be aware that the Denver area street grid includes major, multi-lane streets about a mile apart, running both north/south and east/west. This can be an easier way to get around (and out of!) Denver, esp if you want to leave via hwy 285 to the South Park, than getting locked into the interstates. A good map is of great value. The Denver area has a fine pubic transit system [rtd-denver.com] so if you need to layover there, I recommend using it.
Grand Jct. If you go to Grand Jct on the Zephyr from Denver the arrival time, assuming it is on time, is around 5 PM. Good option, IMHO, is to stay in Junction for the night and get an early start the next day. GJT has an adequate, altho limited(no service on Sunday, for one thing) , bus system[gvt.mesacounty.us] so it is fairly easy to get to a motel. Most of the car rental outlets are at the airport so a motel relatively near to it is not a bad idea. I usually have used the Motel 6 there (#110, IIRC) but see above on my motel requirements.
Albuquerque: Of the three, the one I have used the least. It has a decent public transit system[cabq.gov/transit]. I've only gotten off Amtrak once there and I chose to get my car and drive north to Bernalillo, NM (where the road to Farmington and Durango leaves I-25) and spend the night there so I can't help on motels. There is/was a nice Motel 6 at the Bernalillo exit. Also, although I haven't had opportunity to use it, there is the Rail runner service to Santa Fe [www.riometro.org]. And a final(NNG, Not Steam, sorry) note: The Amtrak service east of ALB to Trinidad, CO is currently something of a political football and may have it's route changed or replaced by a connecting bus. If you have a yen to ride the old AT&SF over Raton Pass, it may be gone soon so...
On going from GJT to Durango I would note that hwy 550 from Ouray to Silverton can, at times, be a bumper-to-bumper mess in the summer, CO 62/145/US160 following the RGS route is usually less congested except for the area near Telluride. At least it used to be that way.
As I've said before I highly recommend good maps, both for planning and during a trip. I find US Forest service maps highly useful, online maps don't seem to work as well for me.
More generally, there are a lot of things to see and do coming from/going to any of these options, depending on how much time you have and how willing to get off the main roads so it is hard to recommend a certain route. On my last trip, as an example, I got off Amtrak at ALB, spent my first night in Bernalillo, and then wandered up the road to Farmington as far as Cuba, NM. I then went to Antonito via: NM 96, US 84, NM 554 and US 285(all paved). Pretty drive and it allowed me to check out parts of the old La Madera Branch(abd 1932) enroute. I spent 3 nights in Antonito with a round trip on the C&TS, explorations of the north end (to and a bit past Taos Jct, road to Barranca was closed for repair) of the Santa Fe branch and some of the first few miles of the La Madera branch. I then went north to Salida (one night), drove up to the Buena Vista area to check out DSP&P Trout Creek canyon area, back to Salida and over Marshall Pass to Gunnison(1 night). Note: all of these (except the CATS ride) involved some gravel and/or dirt roads and hiking. Then, on the way to GJT, revisited Black Canyon sites, poked around some side roads just west of Gunnison and spent the night at GJT. Last day I started out by exploring west of GJT, including the first few miles of the Uintah and the original D&RGW Ry grade as far as the Utah state line. (Early in the morning to beat the heat!) Then I went back to GJT, turned in the little Ford Focus I had rented (after cleaning it at a car wash!
) caught the GVT bus from the airport to the Amtrak station and headed home. All of the explorations I mention leave me wanting to go back and look deeper/farther, BTW. This was in 2010, someday I hope to be able to afford a scanner so I can scan in and post some of the pictures I took. (yes, I still shoot film)
Given your time allowed and what you most want to see/do I'd be happy to make some more detailed suggestions.
hank