We dived Gizo & Uepi a couple years ago. Gizo is incredible. Danny & Kerry Kennedy are the best. We thought the diving there was better than Uepi, but both are good. You can dive with the house reef sharks at Uepi, which is pretty neat.
The Bilikiki stays more in the eastern Solomons. If you do the boat, see if you can take a few days to go to Gizo, too.
The Australians we met liked Vanuatu, but thought the Solomons were better.