My favorite is Pacific Rim Divers. Patrice (Owner/DM/Capt.) is great, it's like diving with a friend (which pretty much is true at this point). I have dived with Pac Rim three times now, and every time has been great. We were on the Big Island in August, and we always stay in Waikaloa. Pac Rim is boat only/no shop, but rents gear if you need it. The drive from Waikaloa to the boat harbor takes about 35-45 minutes because of inbound traffic into Kailua town but we dont mind. Pac Rim has a six pack only boat with fresh water, and light snacks, including Patrice's killer home made brownies. Patrice has saint like patience with new divers, but respects the abilities of more experienced divers. She has a great eye for critters, especially tiny ones that some others may miss. Pac Rim is always my #1 choice on the BI.
Other good choices are Big Island Divers, Kona Honu, and Jacks. If you are going to do the manta dive, Kona Honu runs a very good trip. The boat looks a little "cattle boat", but they dont over do it with divers and some like the bigger boat at night if they tend to get a little green around the gills.
You will find that the operators on the Big Island run very professional, fun operations that take pride in their work. Suprisingly, there are not alot of dive operators there so it is a tight knit community that work well with each other, even as competitors.
Have a great time on the Big Island! Feel free to ask any questions about that incredible place!