The Big Island is my favorite place to visit.... done it many times. I am not a beach person... so I am not a fan of staying on the Kona side... you are far away from the beauty of the Island... and would have to travel a great deal to get to the northern/eastern/southern areas.
Personally, I would rent a condo/house on the Hilo side of the island and use that as home base. So much more convenient to the sites that are most worth visiting.
Also, I would get a 4-wheel-drive.... and I had no problem using the car from the company we rented from... was not Harpers.
I highly recommend this tour. FREE. And the only way to get inside one of the observatories. I have done this four times... love it each time.
http://www.ifa.hawaii.edu/info/vis/v...mit-tours.html
Lots of great advice in the Hawaii forum.