Don't worry too much about the flight. Before my HNL <--> Orlando flight, I spent hours worrying about how my 2yo and 7mo would handle the long ride but found comfort in knowing that I would have a lifetime of spectacular memories and pictures - such a small price to pay for 12-15 hours on the plane.
Here's another vote for Hilo even though it's no where near as upscale as Waikaloa or tourist-friendly as Kona.
The Naniloa is the nicest hotel in Hilo, but it's far from nice - even after the renovation. If you get a vacation rental, check to see if it has A/C because Hilo can be very muggy.
Imo, Hilo is as close as you can get to "real" Hawaii. Hilo is the real life version of the laid-back, small-town life you see on postcards of Hawaii. The vast majority of residents are locals, most of the businesses are mom-and-pop or local chain stores, and the restaurants still serve classic, local favorites. None of that rice pilaf, kobe beef patty with pan gravy loco moco weirdness that's oh so instagramable and trendy lol.
Hilo has awesome parks, lagoons, and beaches for your kids to explore. There are also a number of community events such as the Merrie Monarch Festival, the craft fair at the tennis stadium the weekend before Thanksgiving, and the weekend farmer's market.