Fiji's great for diving, there are budget accoms in Kadavu and probably affordable places on Taveuni.
Forget Vanuatu for the diving except for the pres. Coolidge wreck in Santo, otherwise the archipelago landside is probably the best you can find in the south pacific for genuine culture = PNG+safety
New Caledonia can provide very good diving too, although the place in generally very expensive, you can lodge in bungalows/guesthouses in the outer islands for more affordable prices and the diving may be as good as well.
I know a member of this site is opening a new dive center in Lifou island, which is supposed to cater outstanding diving from all the feedbacks I read, you should consider contacting her for more information.
French polynesia is supposed to be a Mecca for shark diving with places like Fakarava and Rangiroa. Don't expect much with corals though.