LOVE LOVE LOVE KONA!!!
lol... sorry. When I went with my family (parents/brothers) while I was in college we went to the Big Island. We actually traveled all over the island and stayed a few days in each area. We were there for two weeks. We started and ended in Kona, and it's a wonderful city.
I WOULD say that you have to go out to Volcanoes National Park, but I don't know how mobile your dad is. You could always do a night trip out there, though, and at least watch the live flow from the entrance. Doing a day trip and hiking out to the live flow, though, is likely to be beyond what your dad is capable of. It's not an easy hike, and there aren't exactly any trails.
Check out the lava tubes if you can (hollowed areas that lava once flowed through).
Be advised, a lot of restaurants don't have liquor licenses on the Big Island, so they don't even sell beer or wine.
This place is really neat, and should be easily accessible for everyone, if I remember right. http://www.letsgo-hawaii.com/heiau-hawaiian-temples/
In (or around) Kona, there's a place you HAVE to go (if you have this kind of sense of humor!). http://www.alohahawaiianstore.com/ The website says they're 8 miles south of Kona. :) Donkey Balls are THE BEST!!
There are several different plantations that do tours, I believe, so that could be neat, too.
There is just SO much to do on that island! It's also where most of "Jurassic Park" was filmed!! :)
ETA: They've got tons of different kinds of beaches on the Big Island, as well. I can't speak for the others islands, but I know the Big Island has white, black, green, and your typical "tan" sand beaches. The black and green are the most unique. http://www.gohawaii.com/big-island/regions-neighborhoods/... This looks like a pretty popular/easy access one. The one we went to was WAY off the beaten path and we were the only ones there, but you had to hike across an old lava field, so not something everyone would be up to.