Big question is, have u built points? If not, maybe start with Colorado. That way in a year or two, you all can draw the same unit as a group. Your not going to find OTC mule deer tags for nonresidents in the typical western mountain hunting states (CO, WY, MT, etc). The Frank was mentioned for Idaho but good luck trying to use that online "OTC" system when tags go on sale and think u will be able to get the same unit with other guys (if you all even make it into the system and out of the waiting que)
OR you can take the advice of others and hunt other states that have mule deer where tags are easier like the Dakotas I believe (do not know much about). Arizona also has OTC mule deer tags.
And yes GoHunt is a great tool for all of this information. Definitely recommend if you really want to get into it.