Greg, your question piqued my curiousity. I tried to dig up some info from the H-DOT website on bicycling, but it's got to be the most disfunctional government website i've ever seen - just a mass of dead links, at least in the cycling arena. I couldn't even find an email address to complain about it... They suck beyond belief, just wish i could tell 'em that.
I've been to the Big Island, driven pretty much around it, but haven't biked at all on it. Not sure what to make of the cycling conditions; wish i remembered more about whether or not there's shoulders (when i drive i habitually watch to see if there's a decent shoulder) but really can't recall.
There's some pretty remote areas on the north and south sides where it *seemed like* the traffic was fairly low. There may be some opportunities to get off the main island ring road on to some tertiary paved back roads, which could be really cool. the landscape on the north side - on the way from Hilo over to the dry side - is really beautiful, seems like it would be fantastic for cycling.
If you go, report back!