As of now, there are no alternatives to flying between islands (with the exception of Maui and Moloka‘i), but there are alternatives to Hawaiian and Aloha Airlines. Pacific Wings, Island Air, George's Aviation are a few who service the neighbor islands, and although they use prop planes instead of jets, their prices are usually cheaper then what's offered by AQ/HA.

You could also take the Pride of Aloha (search will bring up a thread) that's the new cruise line servicing Hawai`i. This would allow you to see all four main Hawaiian Islands within seven days (leave Sunday, arrive Sunday), spending about a day on each. Might be another option.

Until that new ferry comes along, though, it's fly or bust.

aloha