Ok, on the western side of Fiji there are all the main resorts, where everybody goes to. On most of these islands, the only thing 'Fiji' about it is the location. The coral is often all dead, so when you go snorkeling, all you can see is dead grey coral at a lot of these island resorts. Sure these places are good to take the kids, maybe just to lay on the beach all day, but that's all the 'Fiji' you get.
Taveuni is a big island. Not many tourists choose it as their holiday destination as it is usually too far out. Because of this, tourism has only mildly effected the island. You will see a beautiful untouched side of Fiji that many people never see. The scenery is endless. But I do suggest also staying on a western island for a few days.
When going into Nadi town, make sure you stick to the main shops. I suggest Jack's Handicraft for souvenirs and also the shops full of tourists. Restaurants are ok. I know people who have walked into other smaller souvenir shops in Nadi, and haven't come out with their wallet and belongings. Be careful with taxi's, although they are cheap, make sure the driver always use the meter. Some locals will do anything to rip you off.
In Taveuni I suggest the Taveuni Island Resort. But for variety, stay at more than one.