If you drive down to Cincinnati (CVG), you can usually find flights with just one layover (via Atlanta or LAX) on Delta. I highly, highly recommend doing this, even if it's a hundred bucks more expensive than flying out of Dayton. Every layover adds a few hours onto your trip, and increases the chance of delays. (If you fly out of Dayton, you should be prepared for two layovers no matter what airline you fly because you'll have to fly to that airline's regional hub first, then to their western gateway.)
Whether you call for tickets, or book yourself on Delta.com, know that you can usually fly into one island and out from another on the same itinerary, for just a bit more than if you flew into and out of the same island. This negates the need to return to the island of your arrival (including the added costs and time to puddle jump to that island) in order to return home.
LIH->OGG (Hawaiian Air)
The first and third flights are considered a RT flight. (In order to book on Delta.com, select the option for "Multi city."