I guess its a bit tough to determine what an "off the beaten path" mission would be. Sometimes when I'm traveling, I get distracted by groups of bandits/trolls/dragons, etc etc. But as far as missions go, ususally my random one are the "miscellaneous" missions.
Of those, my favorite so far has probably been the Mysterious Haunting rumors in Shroud Hearth Barrow. You get the quest from the Inn Keeper in Iverstead, and then go down into the tombs only to discover a thief has been using potions of the phantom (?) to make himself appear like a spirit. He tries to drive you away, but killing him reveals his plan to obtain the treasure in the tomb using a claw (similar to the golden claw used in the riverwood quest). The quest is small potatoes, but it was entertaining from a storytelling aspect, and the loot was fairly good.