My boyfriend and I went to the Big Island a couple months ago. I reviewed all the places we went on yelp and made a list here: http://www.yelp.com/list/big-island-for-vegans-honalo-2
Stay somewhere with a kitchen. You may want to bring or buy a good knife, since most rentals have shitty knives for cutting up the fruit. I suggest spending at least part of the time on the Hilo side -- it's closer to Volcano Nat'l Park and the viewing area (if it's still happening or open when you go), plus fewer tourists go there. I actually had more fun on that side and we rented a house, which rocked. Like someone else mentioned, there are tons of health food stores, not to mention the farmers' markets. And fruit stands. Holy shiitake, so much fruit. <3 <3 <3
The southern part of the island is also probably worth a day of exploring -- pretty sparsely populated but some really amazing things to see (and I think there is a small market in a town down there, but it wasn't on the day we drove through).
If you are into coffee, do a little research about the myriad coffee tours offered in the Kona growing area (well, there are some outside it, but they are chock-a-block up there). I found that most of the beans were ridiculously overroasted -- honestly, I didn't have a single great cup of coffee in Hawaii. The tour I went on was pretty boring, and the only thing I learned was that peaberry coffee is kind of a scam.
If you are into biking, which I am not but my boyfriend is, I can get you some notes about that. Well, he's into road biking -- and regretted not bringing his bike into Volcano -- but it seems like you could go more places with a mountain bike.
There are a zillion little corners and sights to see. Go, explore, enjoy! Just have a kitchen and get some basics and you'll be set for food. The restaurants weren't where it was at for us, anyway.