We were on the BI for a week in June and we loved it! We stayed in both Kona and Hilo because we wanted to experience both sides. In Kona, we stayed at the Royal Kona. The room we stayed in was quite dated, but the location was perfect for us, and having an ocean view was worth everything. They are in the process of updating rooms, too. You can walk to tons of places to eat, Kai Eats and Drinks and Huggo's are good, but Huggo's is quite popular, so you probably will have a bit of a wait. There is an ABC store very close by, too. Most importantly, the view for the sunset is amazing here.
Here's a quick overview of what we did:
We love National Parks and National Historic Sites, and our favorite NHS were Pu’ukohola Heiau and Pu’uhonua o Honaunau. We explored those and also stopped at a coffee farm.
We took the southern route to get to Volcanoes NP and we stopped at the Kahuku Unit of VNP and did a small hike into a cinder cone which was really fun, stopped at South Point, which is the sourthernmost point in the US - super windy and no fanfare, but lots of people cliff diving/jumping, and if that's your thing, it could be cool. Punalu'u Bakery and Punalu'u Black Sand Beach are worth stopping at. We didn't get to the Green Sand Beach and I think that would have been awesome.
Volcanoes NP is 100% worth spending at least 1 day here! The lava tube, Crater Rim, steam vents, and the Chain of Craters Road are all beautiful! We stayed one night in Volcano House.
In Hilo we stayed at SCP Hilo Hotel which was very nice. We stopped at the Hilo Farmer's Market for some souvenirs, drove up the Hamukua Coast to see waterfalls, rain forests, Waipio Valley Lookout. The Mauna Loa Macadamia Nut Factory is on this side of the island, but we missed it. We did stop at Big Island Candies, tho.
IMHO, if you can swing it, I think you should stay on both sides of the island. Kona is very touristy, while Hilo felt like it was where the locals live.