Kauai - Fathom Five Divers in Koloa was good op. Well organized, good staff, with good communication through email. Easy 25 minute drive from where we stayed on the east side to their location on the south side (where most dive sites are.) If right time of season, Niihau is considered by many (I have no experience) to be a good area to go to from Kauai. Depending on your preferences, some ops will take you there, but there is an op somewhere closer to west side that has a fast boat, so cuts the trip time down quite a bit. Staying in Koloa or Poipu area puts you close to dive ops - most dive sites are on south side also although there are some sites on other sides of the island.
Big island - Jack's Diving Locker in Kailua-Kona was a good op. Fun crews. Could meet at shop in town and ride to marina or meet at their small shop at the marina (which we did as we had a car.) We got some good whale watching in during surface intervals. Lots of volcanic topography and some larger sea life to see. They also do the Manta Ray Night Dive. *Just my 2 cents here - we did the manta rays as a snorkel as we had 2 non-diving wives- it's cheaper and you see the same thing - it's either mantas coming up to the surface to greet you before making a u-turn and heading back down or vice versa if you kneeling on the bottom - not much of a dive IMO. One positive though is there are less people doing it as a dive, where at the surface, you can be surrounded by lots of people.
Also on the Big Island, Waikoloa, about a 30 (+ or -) minute drive north of Kona is a nice area. Blue Wilderness Dive Adventures shop is located in the Queen's Marketplace in the Waikoloa Beach Resort, but their boat - a RIB - leaves from Puako Bay about 10 minutes away. Their procedure of donning and doffing BC's in the water quickly became a favorite for me (maybe not everyone else though.) Smaller coral reef heads and smaller sea life - saw a few new creatures.
Can only compare the 2 islands as my dives were cancelled when on Oahu. The Big Island gives you more sites and variety than Kauai, so if it is a 2 week diving trip, Big Island would be my pick. Although I mentioned the 2 ops I dove with, there are many that get good reviews.