Have fun on your tour! My wife and I have been going on tours on our tandem for the last 10 years. Our tours have mostly been in Europe, where the road network is very dense and signing can be interesting. Our first two tours we used paper maps, but spent a fair amount of time looking for our route. After a tour in Germany where we turned our first 47 mile day into 87 miles (in a cold rain, too) our next tours used a gps unit. We seem to pass a fair amount of people who are puzzling over maps, but to be fair there are probably just as many who are following their maps at speed.
I use a Garmin Edge 1000 (overkill for most touring situations) in the front, and my wife has a Garmin Edge Tour model in the back. The Tour model is probably the best fit if I didn't do other types of riding as well. I find that navigation is easiest for me in the front, but we have friends that have their gps units in the back with the stoker.
We also carry a paper map that would allow us to continue riding if our batteries died, but we haven't had to resort to it--a compass is handy in that case, but there's one on your smartphone. This map isn't in sufficient detail for comfort, but would be helpful in figuring out intermediate towns and then supplement it using highway direction signs.
In the US the road network isn't nearly as dense as Europe, but going through cities a gps unit can let you use city streets or bike routes that aren't nearly as busy as the main roads. It would be very difficult to carry enough maps with enough detail to show named city streets for the entire tour, and searching for maps may be time-consuming or fruitless.
Have fun,
Mark W