Was there 3 years ago as a so called gucci-backpacker, in that I wasn't looking to rough it but didn't want to spend a fortune. The outer islands are definitely the place to head to, went to the Yasawas, which you can get to using the Yasawa Flyer, a ferry that visits all of these islands on a daily basis, making island hopping relatively easy. It is remote in that you won't have internet/phone access when out there (unless things have changed dramatically), but definitely the most relaxing experience I ever had, after 2 days I had completely forgotten the office and all its stresses. The Fijian people are extremely friendly. There is a good mix of high end sky-is-the-limit luxury and mid price $50 per night. Accommodation on these islands is usually in what is known as a 'bure' i.e. a little wood cabin for 2 people.
If you are looking for luxury, avoid Beachcomber Island, which is overrun with backpackers. Also avoid spending time in the capital Nadi, which is a bit of a dump.
The Thorn Tree forum on lonelyplanet.com is a great place to pick up information on resorts, prices etc.
Have a great time