I get up there once a year to visit my grandpa. It's an awesome, beautiful place. I would definitely live up there if there were more programming opportunities and more people I knew.
Best of luck to you!
It is the kind of city that turns everyone into a walking advertisement — even the folks who eventually leave tend to come back to retire.
You might look into companies like Submittable (who are based out of the area) if you're looking for programming gigs. They're working hard (with what seems to be a very collaborative and willing government) to flesh out the area's tech infrastructure, so keep your eyes open for more opportunities thereabouts over the next year or two.
And happy to introduce you to some wonderful folks in the city if you're ever stopping through and want to make some friends!
Closest airport that I would consider 'major' is Seattle, which is a solid day's drive (about 7 hours). You can get anywhere from Missoula's airport, but you'll have to stop through Minnesota, Seattle, Denver, or some other major hub. Adds a little cost, which is a bummer, but still possible, and even for someone who travels all the time like I do, it's not a deal-breaker-level inconvenience.
Amazon-wise, it's just as fast as anywhere else I've ever lived. I have a Prime account, and often receive my packages the next day.
I'll also add that the internet is some of the fastest and cheapest I've found outside of areas that already have gigabit up and running.
I also kind of dig the clean, chilly weather they get during the winter, so I'm a bit biased on this question. I don't know that it gets as cold as someplace like, NYC or Chicago, though, which is something :)
They do have a solid community, though, from everything I've heard so far. http://Startupbozeman.com has some info, and I went to the HATCH conference this year (http://hatchexperience.org/) which takes place in Bozeman, and met some wonderful representatives from the city. Good people, a nice downtown, and though not QUITE as walkable or cheap as Missoula, it's absolutely beautiful over there, and I always enjoy a visit.
Recently started up a non-standard publishing company there, and the culture is stellar, it's a college town (full of culture and young people doing fun stuff), very low cost of living (rented a massive house with a bar/cafe in the basement for about $1400/month), and zero sales tax.
Quality of life is best I've found anywhere in the US (and I've been to all contiguous 48 states several times, looking for places to set up offices and live when I'm not overseas). It's incredibly walkable, has a nice downtown, very active, athletics residents, and folks care about their health (which is manifested in both their activities and the local produce/restaurant/food culture).
Happy to answer any other questions anyone might have about the area, and to introduce you around if you end up moving thereabouts :)