Stopping in Honolulu
The only way (as of early 2006) to get to the Big Island from Honolulu is to fly, either on an interisland flight or on a charter flight. Some airlines fly directly to the Big Island, and some go to Honolulu Airport first and either connect you to the Big Island or expect you to find your own way. This could cost you anywhere from $50 one-way to over $100 one way if you have to find your own way.

Flying Direct to Hilo or Kona on the Big Island
Major airlines that fly into Hilo are ATA, and Aloha and Hawaiian (these last two are from Honolulu only). Airlines that fly into Kona are: Aloha and Hawaiian, American, Delta, and Northwest. See my post Who flys where in Hawaii on my Hawaii Flight Prices blog for more islands and links.

*** These are sample prices, they WILL be different when you search!

Fly Direct to Hilo

Fly to Honolulu (connecting flight roundtrip will add approximately $140 in most cases)

Fly Direct to Kailua-Kona

Fly to Honolulu (connecting flight roundtrip will add approximately $140 in most cases)

Summary - So, flying direct sometimes gets you deeper discounts, sometimes not. Use a fare comparison engine like Expedia's for easy compares.