Hi Scuba KBell - We've been to Fiji 8 times and have our 9th trip planned. Greg gave you some great advice - if you want really good diving, skip the Coral Coast. And if you want to do a lot of diving, you will lose dive days by changing resorts, especially if you fly. When we go, our focus is diving so we don't change resorts.
With the exception of Rakiraki area (Wananavu and Volivoli resorts), the diving near the island of Viti Levu is not that great. There tends to be a lot more runoff from rain around Viti Levu than the smaller islands. Beqa diving is good but the weather closer to Suva is rainier and rain runoff definitely impacts viz inside Beqa Lagoon. The Rainbow Reef off Taveuni is very good - mostly drift diving due to currents but the soft corals there are amazing. Kadavu has great diving too. But Both Taveuni and Kadavu require flights. We didn't think the diving was as good in the Yasawas or Mamanucas but their advantage is that you can get there without an airplane ride. A less-known dive destination is Naigani Island. It's not fancy but the diving was excellent and we never saw another dive boat in 20+ days of diving on two different trips. You get there by flying to Suva, then having a 90-minute van ride and a half hour boat ride.
When booking at any Fiji resort, enquire whether they allow diving on Sundays - the chiefs of some islands don't. Also, if you aren't bringing your own gear, some resorts have fairly new and well-maintained gear and others have scary gear. After our first trip to Fiji, we decided to always take our own gear to Fiji.
You asked about kitchens - there were kitchens at Volivoli and Naigani. You'd need to bring any food you wanted to cook to Naigani as there is no store. There are a few small stores in Rakiraki about 10-15 minutes drive from Volivoli -but we usually just buy the resort's meal plans and eat there. They're generally reasonably priced and so much easier. Plus if you are on a small island, they are often the only place to eat.
Finally, we always take any over the counter or prescription medicines we might need including cold remedies, anti-biotic ointment, anti-diarrhea meds, etc.
Virtually all of the islands that have diving have great beaches so you don't have to do either beaches or diving. The smaller islands give you a better feel for the "real" Fiji and usually offer village visits, Meke dances, Lovo feasts, etc. But the remote islands are pretty quiet so if you like nightlife, the coral coast or Denarau could be a better option.
I hope this helps you - if you have questions, you can PM me.
Cindy