We have at least one Insider that spent some time last year at Mauna Kea so let's see if bejacob will be able to help answer your question?
In the meantime, quickly taking a look at googlemaps it appears there are a few spots north of the resort:
With Waimea about 12 miles away you should also be able to find some spots to dine there.
Thanks for the shout-out IAHFLYR.
The Mauna Kea is pretty isolated which is part of its charm. That said, you won't be too far from several areas where you might find some interesting food options.
The closest is probably the half-dozen restaurants in tiny town of Kawaihae about 4 miles to the north. Cafe Pesto, Blue Dragon, Kohala Burger & Taco, and the Aloha Deli are all located there. I can recommend the last one for an inexpensive breakfast.
Not too much farther (though the other direction) are the Shops at Mauna Lani. There is an amazing vegetarian place called Under the Bodhi Tree, as well as a Ruth Chris and a Tommy Bahama (if you want chains). I don't recall what else, but there are a couple others. That's maybe 15 minutes by car from the hotel.
Just a little farther is the Queens Marketplace complete with food court. That also puts you close to the Marriott at Waikoloa and the nearby Roy's Waikoloa Grill and Three Fat Pigs (gastropub). There are quite a few more options in this area.
About 20 minutes (head Mauka - inland) is Waikoloa Village. Island Lava Java has some good menu items (they also provide catering for some of the tours - decent wraps and sandwiches). I don't recall too many places here, though I seem to remember both a Thai place and an Italian restaurant.
The last area I'd mention is the town of Waimea on the way toward Hilo. That's about 25-30 minutes, but you'll have quite a few options here. I tried the Big Island Brewhaus and thought it was decent. Village Burger is reported to be pretty good. Waimea is also the home of Merriman's, Chef Peter Merriman's flagship restaurant.
Anyway, that gives you a few places to explore that aren't too far away. If you want to drive down to Kailua-Kona, there are even more choices. Let us know of any interesting places you discover.