There are two main towns on Viti Levu you can visit on the side of the island nearest the airport, Nadi and Latouka.
Nadi, which is five miles away from the airport - I found a little less interesting and a little more catered for tourists. This is where you find the 'sword sellers' (the Fijian term for the local, pushy market sellers)
Though I have heard that this is also a problem in Latouka, and all areas tourists may go in Viti Levu, I never had the experience once. I did, however, avoid Nadi except to to to and from the hotel and pop into the market for some groceries to take on the road. The other travellers we encountered said they had a lot of problems there with the sword sellers, cheezy market products, and taxi drivers.
Though the Lonely Planet guide suggested you would be accosted the minute you walked off the plane, we didn't find this to be the case. I found the pushy markets infinitely worse in other places, such as Spain or other Mediterranean countries.
However, as I've said - I did hear from other travellers they had problems in Nadi. It is worth mentioning here because of the specific 'sword seller' technique to scam tourists which involves a 'friendly' local Fijian coming up to tourists, chatting with them for a few minutes, eventually getting their name which they then immediately carve onto a little wooden sword and try to charge $20 for. It is, unfortunately, best to dismiss yourself quickly and be on your way. And don't offer your name.
I normally would advise in such a situation to simply make an effort not too appear to look too much of a tourist - but in Fiji it's all but impossible to disguise the fact. There's no real doubt who is and isn't a local in Fiji - no matter how comfortable you may look in the setting. Still best not to flaunt the 'tourist' angle in these towns, but either way you are still going to stand out as someone who is not a local, so do be aware.
But don't let this worry or effect your plans for your trip. It's not as bad as it sounds, and as I said - the entire time I was in Fiji I never had any problems with it at all.
The little local town of Latouka is probably the better option in my mind. We took the local bus the 15 miles from Nadi into Latouka, and though it took over an hour - was a great experience and for the first time in about 6 months of world wide travel, we were the only people for miles who were visitors.
Latouka seems a predominantly Indo-Fijian town. Almost every shop (of which there was a large selection) was an Indian shop, and there are plenty of places to go for different types of Indian clothes. I went looking for a traditional Fijian sulu (my jeans and boots were simply no good here) but ended up buying two long, cool Indian style skirts - one for me and one for a friend back home. These were very nice and about $7 each.
I wouldn't say that Latouka was very cheap - as some of the other travellers assured us. It was reasonably priced, though and really not targeted for tourists, as in the entire day we spent there we only saw two other non-Fijians. It was great.
The bus stop may look a bit daunting and rough - but the atmosphere is fine. I wouldn't recommend using the toilets if you can avoid it, but there are lots and lots of families and locals coming to and from town - and I never felt uncomfortable. (Except, of course, by the stifling heat; which was so much worse in the town.)
We had lunch at a hot little restaurant simply called 'Country Fried Chicken' and had very, very dry chicken, a coke and an ice cream. The place was nearly empty - but the price wasn't too bad (a few Fijian dollars each) and the owner came over twice to try to get the rattly air conditioner over our heads to pump out some cool air. They were extremely friendly and helpful.
It is, however, very hard to find local Fijian wares here or anywhere it seems. We went extensively through the large Fijian market next to the bus station and not only was the selection bad, and exactly what was in all of the gift shops, it was actually More expensive. Unless your resort has a very good gift shop - you might be best off getting your souvenirs from the airport (of which there are actually some good options. I highly recommend the Pure Fiji and Renue coconut oils - they are amazing.)
Latouka is also good for banks and post offices. There is a bank coming into town where you can exchange travellers cheques or get money out of your account in the cash machines, and it is very clean (and cool) and well guarded.
The post office is also good, has some excellent post cards (the only I could find in town) and you can get your stamps right there.
Though it's not a pretty town, there is a park (which was largely filled with families dozing in the afternoon sun) and a bit of waterfront you can sit by and have your lunch or try to cool off a bit.
Of the two, I would have to recommend Latouka as the little local town of Viti Levu to visit while in Fiji.