Most accommodation in the Nadi area tends to be around Nadi Bay. That beachside strip is packed with budget priced hotels and resorts, and is only a 10-15 min taxi ride from the airport.
But accommodation in the heart of Nadi? Nope, very little, and certainly not budget priced. The only exception is the Nadi Downtown Hotel.(previously known as the Nadi Downtown Backpackers). Not only is this situated right in the center of town (so very close to banks, supermarkets, internet cafes, restaurants and bars), It is Under new management.
Previously, this was just somewhere to stay if all you wanted was the cheapest bed possible, and didn't care if the roof was leaking or things didn't work. But things have certainly changed for the better recently with a new owners.
The rooms range form a single with A/C up to very family rooms that can sleep 2 adults and 3 children. Prices are per night (prices in Fijian dollars, and correct as of March 2014)...