I would stay as long as I could. It is a BIG Island. I spent 5 nights on Maui last year, and felt it was plenty. I have been to the BI 4 times now, and still have not seen the entire thing. It is MUCH more variable as far as landscape than Maui. Have you done any research on it? Something like 13 different climates on one Island. Mauna Kea Resort is a great base. The only reason I can think of to book a night somewhere else, is if you want to see the volcano after dark. I might book a night or 2 in Volcano itself, and in Hilo for that. Lower Puna is very scenic, I can easily spend a full day down there. Pretty much everything else can be done on day trips from Mauna Kea Resort, although some of the days might be long.
Definitely do the Manta Ray night snorkel, and I did enjoy a drive to the summit of Mauna Kea, although heed the warnings about altitude sickness. I was surprised that it affected me as much as it did (only went as far as visitor center), and probably will not go back up the mountain for that reason. You will find lots of restaurants in places like Waimea, Waikoloa Resort, etc.