I'm not sure about the rest of it, but it certainly is not flat in the Washington part.
That's for sure. The NT route in WA includes Sherman Pass, which, if I am not mistaken, is the highest paved road in the state. You would then climb Waucunda (sp?) Pass (not that bad east to west) Loup Loup Pass (some steep sections on the east slope) and then, as mentioned, the Cascades. I agree that's it's a great area to ride. I found in-town camping in Ione, Colville, Republic, Tonasket and Withrop. Made getting groceries, etc., very convenient. And SR 20 through the Cascades is fabulous.
I went west to east, but working backwards in my mind, MN and ND were fairly benign hill-wise (note that AC is rerouting the NT in ND so things may change) as was "The High Line" between the MT border and Cut Bank, although killer headwinds could make up for the relatively flat terrain. If you followed the route proper, you would cross into Canada on the way to McGrath. That's a lot of rolling terrain. From there towards Waterton Village is also rolling. Chief Mountain Highway back into the U.S. is not easy. Just rode it again in '09. There is a steep 5-6 mile climb at the very start, and then some hills before and after the border crossing. From St. Mary, MT you enter Glacier N.P. and climb to around 6,700' to Logan Pass on Going to the Sun Road. It's not killer, and can be broken up by staying at Rising Sun Campground. It's worth any effort that it takes. Arguably one of the most scenic mountain roads in the U.S.
The other option would be to detour off the route to East Glacier and take U.S. 2 over Marias Pass. It's a 12 mile climb and is pretty gradual. A shop owner in town told us it it's the lowest road crossing of the continental divide. Not nearly as scenic as GTS, and there can be some truck traffic. Aslo, from the pass to W. Glacier is a long (54 miles if I remember correctly) trek to W. Glacier. There is not much steep downhill, and even some more climbing in a few places.
The next major hilly section is along the shore of Lake Kookcanusa after you leave Eureka, MT. It's been a while, but I remember some severe rollers. After that, it's not bad until you get to Sherman Pass.
If you opt instead for Missoula via the NT, at Columbia Falls/Whitefish you can take the Great Parks route to Missoula. Did that in '00 and don't remember it being difficult.
