My three all time favorite northwestern towns are Bend, Bozeman and Boise - all are killer mtn biking towns with great scenery, great riding, microbreweries, coffee houses, attractive people... I try to hit one or two of them every summer.
But as for your specific request - Missoula is a great small city, lots to do, university, close to National Forests. It does have some significant traffic due to the two major highways going through, and IMHO, not quite as eclectic and interesting as Bozeman, maybe because it is bigger, but still very nice overall. Weather is very good. It would be a really great place to spend a summer.
Boise is also a great town - the downtown area and surrounding neighborhoods are clean, lively and fun, with great restaurants and coffeehouses, and really friendly people - I really like it and the biking is great . However, be aware that the greater metro area is somewhat sprawling suburbs, and dry, hot and sometimes smoggy in summer. There is great biking right through town along the river as well as up into the foothills. Paved or trails, both are great and easy access. An hour away by car is absolutely incredible country, either up hwy 55 through the canyon to McCall, or hwy 21 to Stanley, up into the Sawtooths. The scenery really is breathtaking with rivers and valleys and large animals. And access to the Eastern Oregon mtns is good also, and they are never crowded and smell like juniper. The only real drawback to Boise, other than it is getting big and sprawling, is it can be a long drive to any other major city like Portland, the Bay Area, or SLC. It is kind of just out there in the middle of nowhere, but that is fine if the town is a good fit and you are self-contained.
Reno is just not a favorite of mine so I won't comment either way. But it is close to Truckee and the Sierras and closer to the Bay Area than the others if you want that, otherwise I would go for one of the other two.
Don't know Missoula at all, and I haven't been to Boise in five or six years (I like it, just don't know it well), but I live in Reno.
Cycling in the city is like riding anywhere else, mediocre bike lanes, traffic and all. It was a nice, compact place until 8-10 years ago, but the greedheads have taken over, and there's major sprawl now. You used to be able to get out of town in 15 minutes; now it takes 40. Drivers are fairly aware of bikes (there's been an explosion of road riders in the last few years), so that's not a problem, but a lot of local riders have attitude problems, which is creating a growing animosity toward cycling as a whole. It's not really an issue yet, but it's getting there. For what it's worth, I notice that drivers are more likely to yield and be courteous when I'm in mountain bike shorts and T-shirt than when I'm wearing the Full Lance. A team jersey predisposes a lot of people to think you're going to be an a-hole. We can thank one of the local clubs for most of that, I think....
As the city has grown, it's gotten harder to get out of town on a bike, but once you do, the riding is excellent. Donner Summit is 30 miles, Lake Tahoe is less than an hour away, and there are mountain passes (7000-8000 feet) to the north, south and west (east is desert, nice in spring and fall). Pavement and shoulder conditions vary from excellent to downright scary, and we're coming off a very severe winter (worst snows in 85 years), so there's likely to be some damage lingering into summer.
Summer weather will be dry (occasional thunderstorms in July & August), 85-95 in Reno (4500 ft.), 75-85 at 6000-7000 feet in the mountains, but can drop to the 40s or even 30s at night. Humidity is low, so 90 is comfortable riding weather. Nice mornings, often strong west winds in the afternoons. I ride east to work, and it takes me 40-42 minutes to get there. Coming home into the wind can take an hour to 1:10.
Giant VT, Kona Hot commuter, Fetish Fixation ss, Fetish velocita road bike, ATP recumbent set up as human powered snowmobile (2 skis)
Boise is too hot that time of year. I live here. I don't even ride except early in the morning. Mountain biking nearby is excellent once you head up the hill and get a little elevation. But you weren't interested in that. I'd go to the San Juans in WA myself.