Where to stay what to do????

My husband and I are headed to Fiji next month(August). We have done a load of research on the different islands and we just need to narrow it down a bit. We are NOT looking to party, we traveled Africa on public transport and are looking to do something similar in Fiji. We are going for the diving/snorkeling and the only dive we MUST do is the Beqa Lagoon shark dive. We are tossing around ideas for Taveuni, Kadavu and the Lau group. We have 5 weeks, the first of which is going to be spent in Nadi( :( ) with my husbands family and then we are on our own. We are on a budget that isn't very big and I know Fiji can be expensive if we don't look around for cheaper accommodation etc...
So one of my questions is which island in the Lau Group could somebody recommend? Did you fly or take a boat to get there? We know that it isn't the easiest thing to get out to the Lau group.
Is there good snorkeling on Taveuni? We hear there wasn't any and in the north you need to be really careful of sharks(Moon Guide). We have budgeted about 6 -8 dives each and the rest will have to be snorkeling, so we want to make sure we can stay somewhere that the snorkeling is great!
Kadavu has great snorkeling right? And I know the diving is meant to be fantastic as well there on the Astrolabe reef??
Any recommendations are accommodations is appreciated too. We do not need to stay in a resort(would prefer not to) and we would LOVE to stay in a village, with a family anything that can get us to meet local Fijians is what we want the most.
As for the Lau Group any info, recommendations are appreciated!
Thank you in advance for everyones help!
Thanks for everyones help!

Snorkeling on Tavueni was good at Susies Plantation Resort on Taveuni but it has now gone seriously upmarket and is called Paradise at about 10 times the accomodation cost.
There was a cheaper place in the nearby village but not sure of its name.
Saw plenty of sharks when we stayed at the island resorts of Vomo and Matamanoa a couple of weeks ago but they are all harmless and great to see.
Snorkeling was very good at both these resorts but they are both reasonably expensive.
Diving was good at Matamanoa but there was no Dive Master at Vomo at present.
Divemaster at Matamanoa was previously employed at Beqa and said the weather there was no where near as good as in the Mamanuca's.
It rained all day every day we were in Taveuni last year.

Lau Group - I spent 10 days on Vanua Balavu in 2005. Stayed at Moanas Guesthouse - if you Google the name it will come up. Local style bure, good food eaten with family, lovely people. Unless you have unlimited time you would have to fly - there is a boat that goes every 2 weeks or so but does not seem to run to a strict schedule - it was 10 days late when we were there & the local shop was running out of everything. Planes go twice a week - it was Thursday & Sunday then, early morning flight from Suva (over an hour) which returns straight away. Because they do not refuel on the island the seats are limited so they can carry extra fuel - booking both ways in advance is a necessity. You can arrange a local cost for the plane if Carolyn at Moanas does it for you (rather than booking on the internet) - but you have to send her the cash in advance. No banks/Visa available on the island so take all cash.
Snorkelling - not so great just in front of Moanas but they are happy to take you on boat trips. We did 2 - a short one to the south - amazing visibility, and a full day trip to the Bay of Islands in the north which was just fantastic, best I've ever done.
Good walking. Interesting in that the people although Fijian citizens are mostly of Tongan descent & they are preserving that link.
PM me if you would like more information & I may be able to send you some photos.

Check ot the Savusavu area of Vanua Levu. There's a place called Dolphin Bay Divers'Retreat that might suit, and you can get from there to Taveuni very cheaply and easily. Taveuni disappointed us, in terms of cost compared to what was available. You might check the area around Ovalau for some interesting possibilities.

I spent 3 weeks at Dolphin Bay Divers and loved it. The diving is some of the best I've ever done, the accomdation and food are good and very reasonably priced compared to other places in Fiji. It's very laid back and a beautiful spot to spend a few days or a few weeks. Not a party place either and very safe. You can snorkel off the beach too.

I can also recommend Matava dive resort on Kadavu. A little more expensive and upmarket than Dolpin Bay but the diving was great (esspecially manta reef where they do NOT feed the mantas to attract them unlike in the Yasawas), the accomodation a little more luxurious and the food portions huge. While this is a 'resort' (it's very isolated with only boat access or by foot to local villages) , the local's who work there are a pleasure of meet and will take you for walks etc if you want.

We couldn't get a flight to the Lau group when I was there last - there was only one flight a week and it was heavily booked so I suggest booking this way in advance if you go.