I think the only thing you are going to find in exerior around here is Fir. That is not bad, but it is heavy. I assume that you are making the sides all in one piece.
The difference between "regular" and "exteior" plywood is the glue, for the most part.
Look at this site: http://www.lumberproducts.com/Products/ ... lywood.htm
They are out of Portland, but have a warehouse in Boise and Salt Lake. There should be a cabinet shop buys from them, (they are wholesale only) in your area. They should be able to help.
They have the best selection I know of, though Intermountain out of SLC has an equal selection.
If you can chisel a bit on the exterior part, there are more options.
If I can help let me know.
dave from the other end of the state