There are parts of Kona, Maui, and Lanai'i that offer excellent diving and while I'm not as keen on Oahu (sorry), the wrecks there are pretty cool. Shore diving is genreally good and readily available, there are lots of endemic species, as well as the manta dive in Kona, and whale songs during parts of the year. The beaches on Maui are awesome, and the islands themselves offer an amazing diversity of activities besides the diving.
That being said, if you're wanting it to exceed Cozumel, you might be disappointed. The density and variety of terrain, visibility, and life in Coz is really hard to beat. Also, the boat diving in Hawaii is very expensive compared to the average two tanker in Coz. Rental car, tank fills and a good map is a good way to get some cheap diving in HI, but it is the ocean, and with your experience you might want to stick with more controlled situations while your confidence increases.
I live in Southern Cal, and while the diving here is ok (amazing to some, but too cold and not enough viz for me) being able to dive where it's warm and clear almost all the time while enjoying an a vacation that includes diving makes HI a slam dunk.
IMHO Hawaii=destination that offers diving whereas Coz=diving destination.
Another thing for me is that every place, and every time you get in the water you have the chance of enjoying and experiencing something new and unique!
Have fun!