Each island is different with unique things to offer. You really won't get much of a feel for each place if you're jumping islands every three days. One dive trip on each island will leave you at the mercy of weather, and where the ops go on their entry level charters. By the end of a trip like that you'll be exhausted, just packing and moving every three days, then add early boat departures, strange beds, and the general stress and exertion of diving - you're setting up a tall order for yourself IMHO! My advice, approach it as a whirlwind tour of Hawaii with a little bit of diving thrown in for spice! Also, the weight of your gear (if your not renting) can be a problem on inner island flights and remember that wet gear weighs more than dry gear - I have been burned on this issue before
During all of the Hawaiian diving I've done, there is a dive guide in the water with you (when you go on a charter), so it's a good place for a newer diver.
This is all JUST MY PERSONAL OPINION and I am in no way an expert, but I have been to all the major islands multiple times and dove on all of them. I prefer reefs, caves, coral, and cool topography over wrecks or sharks so take that into account.
Kona has the best diving overall, a Manta night dive is a truly unique experience. Most of the other Kona sites that I've been too were fairly easy and beautiful. The island is HUGE and unless you are staying close to where the boat is leaving from, expect to spend some time driving. Also, if you plan to stay on the Kona side, but still want to see the volcano, it's not really a day trip - really far to go, plus too high of elevation without an 18 hour time to fly interval. We've been out with WannaDive, and Kona Honu both really good.
Maui has the best blend of topside life and good solid diving. You also have access to Molokini, Lanai, and Molokai for extended charters, each of which have something different to offer as far as topo and sea life. Good food, great beaches, and you can stay close to Kihei/Wailea (for Molokini and good shore dives), or up in Lahaina/Kaanapali (Lanai diving as well as other sites). If you pick a dive op that leaves from Kihei, but choose to stay in Kaanapali, 4:45 am is early to make your 6am Kihei dive boat! We like Lahaina Divers (Lahaina) and ProDiver Maui (Kihei).
Kauai was not my favorite dive spot, but I didn't get over to Niihau which friends say is fantastic! The island is way more chill, and I found it to be a bit boring, but I know some absolutely adore the pace there. The Princeville area and the Kanio coast is breathtakingly beautiful, while the Poipu area is dry so the chance of good weather is higher. We dove with Fathom Five and were very happy. Sheraton Caverns at night was my favorite dive there. I'm not saying it was bad diving, anywhere that is 70+ degrees with great viz is good diving, but compared to Kona or Maui, just not quite the same.
Oahu has wrecks, and a big city, but not really what I go to Hawaii for personally. Some people love the diving there, and I have seen more sharks, and big stuff there than on the other islands. Scottie at Kaimana divers is a popular choice here on the board.
Have fun, and I'm sure you'll hear from others with differing points of view!!