I don't know if you need to look for the least busy roads. Just avoid the busiest and fastest roads and you'll do fine. If I have the choice of multiple roads, I'll usually pick the most scenic or the ones with the best camping facilities. You may have a different set of criteria.
Some years back, I did a little touring in northern Missouri, around St. Joseph and into Iowa and Nebraska. I still have fond memories about that trip. The roads were great for cycling and I don't think there were any to avoid. Traffic wasn't a problem and I thought the area was quite beautiful. You probably wouldn't want to cycle on the Interstate but I don't think bikes are allowed there.
I recall a lot of small hills and some substantial hills in that part of Missouri. One hill by itself isn't a problem but a series of hills can slow down a cyclist, especially when you've got a loaded bike. You may wish to plan your routes to avoid the hilliest places but that's entirely up to you.
I enjoy cycling almost anywhere. However, busy and fast highways are not fun and leave me feeling tense. There are usually alternate routes in most areas. The bigger cities (Kansas City or Omaha for instance) can be a mixed bag. If you know the cities well, you can plan your routes to avoid the main streets or the bad neighbourhoods. You may also wish to avoid certain roads at peak hours
Last edited by Newspaperguy; 02-16-08 at 12:50 PM.
I'm only just getting into touring, planning a mini-tour with motel stops this summer in the New York area. I have a vast preference for roads with few cars on them. The site maps.google.com is an amazing resource -- you can pick a town, then get the satellite view, zoom way in, scroll around, and see exactly what the traffic loads are on each road, and whether there's a shoulder.
Then part of the fun of planning a tour is working out a route that keeps you on decent roads and gets you from "A" to "B". In one place I will have 30 turns to cover a distance of about 12 miles -- and that's only before lunch!
I am also planning a tour of N. MO this spring. I will be leaving the KC area to Hannibal with stops in Linn county and Kirksville. Most of the roads that I am going to take, I have allready ridden on and they are OK for bikeing. There are parts of US36,US65 and US63 that I will not ride on. Most of the state roads are good.
If you are going to be in of the Amish areas there will be wide shoulders.
The only way to know if the roads are safe for biking is to drive them first, but that takes some of the fun out of it.
South of Jefferson City is a nightmare. I dont know of any good roads to ride down there.
I think http://mobikefed.org/index.php has some good info. Also there are some maps for bike tours, but I am not sure where they are. You will have to Google them.
Waterford 1200, Raleigh Record converted to a single speed.
Missouri has some online maps that show traffic counts. You have to combine them with official road maps because the traffic count maps have no towns marked on them.
I too am doing a trip through Missouri. I'm leaving from SW Iowa and traveling to Memphis. My biggest trepidation is getting through St Louis. I think I'm going to use Warmshowers and stay with someone there and use public transport to see some of the sites. We'll see.
Bruce Gordon Ti Rock N Road , Fat Chance Mountain Tandem 
From my earliest touring days I have been drawn more and more to gravel and fire roads for the beautiful scenery they traverse and the usual lack of vehicular traffic. When I ride on pavement I look for the more remote routes if possible. Overall I find this approach more mentally relaxing when I can concentrate on the scenery, photography or nothing rather than vehicles.
I long ago changed from a classical touring bike to a bike suited to any road or non-road. My equipment load is much lighter yet more effective and easier to push uphill on the unrideable portions of a gravel or single track routes.
Adventure Cycling calls this bikepacking I understand. An apt term for bicycle backpacking.
Custom built tourer, custom electric bike, beaters everywhere
Perhaps it's not a good time to discuss coroner's reports but:
When I sat on the City of Toronto Cyling Committee, we accepted a report frpm the coroner about bicycle/auto fatalities. It was long and detailed as such things are but one of the things that came out is that trucks and buses are more likely to be involved in fatal collisions and the other contributing factor was the difference in speed of the bicycle in relation to the motor vehicle.
With that in mind I try to ride on quiet, slow paths and roads far from large, speeding motor vehicles.
That of course does not take drunks into account, so I just assume that every driver is either drunk or so inattentive, that I am totally invisible.
I like wide shoulders. My near-death experiences have come on rides with no shoulders and drivers who seemed to think that an inch or two was plenty of room to give me. Another terrifying moment came on a road with no shoulders and blind corners. A logging truck waited for a suitable place to pass, then got impatient and passed in an unsuitable place, a car appeared in the oncoming lane, and the truck pulled back into my lane, forcing me into the ditch (thank goodness there was a ditch and not a rock wall). I bounced along, inches from the trucks wheels, stayed upright, but broke two spokes. The truck sped off (of course.)
I don't mind a busy road if there are wide shoulders. If there are no shoulders then a lightly-traveled road is crucial. Also crucial is a rear-view mirror. Check for passing vehicles. Then check the oncoming lane and see if there will be room for the person coming from behind to swing wide. If there isn't, pull off the road and let him/her pass. It's a hassle to have to pull off and stop, but you'll (hopefully) stay alive.
I also like roads with smooth surfaces, roads through beautiful and interesting scenery (trees are beautiful, but I've ridden roads in the northwest where there were two walls of trees on both sides of the road for mile after mile. That gets boring really fast.), roads with places to go to the bathroom and get water (interesting juxtaposition, huh?), lots of campsites, etc. A road with a tailwind is especially nice, as is one with gradual climbs and more downhill than uphill.
I don't mind a busy road if there are wide shoulders. If there are no shoulders then a lightly-traveled road is crucial.
Where I live, Highway 3 is a well-traveled road but it doesn't have great shoulders. It's the southern route across the province and so it's used by individual motorists and large trucks and buses. Highway 1 from Chilliwack to Vancouver and Highway 97 between Penticton and Vernon are also busy but they have much better shoulders. I prefer cycling on Highway 3. It seems the motorists there are in less of a hurry than elsewhere and they are willing to move over for cyclists. I've had some close calls on Highway 97 and on Highway 1, I didn't feel all that safe.
on an early tour of Wisconsin --> Michigan UP --> Ontario, CA --> etc...
I would often ask in town for the best way to get to the next town (after having some bad map experiences). Most of the time, I would get some excellent directions up little travelled roads. I recall a route from around Green Bay to Oconto, Wi that was amazing.
I am not too fussy. When I can find them lightly traveled roads with wide clean shoulders are a plus, but I have ridden many miles of shoulder-less roads with lots of traffic, You can't alway have the optimum. There are places where if you want to go there you have to put up with what there is. Yellowstone comes to mind, lousy roads but worth it. Any transcontinental US route I have heard of has some sections of roads with no shoulder and not all of them have light traffic. You just deal with it.
Stokell, there are a lot of facts there that are highly suspect as being applicable to bicycle touring. What happens in the city can be the exact opposite of what happens on rural roads. There are also differences between fatal accidents and (severe) injury accidents. Overall, the likely hood of getting into an accident with a bus or truck on a highway with a wide shoulder is extremely small. This report has a good analysis of cyclists using highways in AZ is interesting: http://members.cox.net/ncutcdbtc/freeway/bkfwcr02.pdf
I will also note that quiet slow roads can be quite safe as well.