The centre of Suva is walkable in twenty minutes from end to end, and most of what you want to see is concentrated in this small area. For anything further out — the university, the Mormon temple, Colo-i-Suva — taxis are cheap and metered. Always check the meter is running, or agree a fare before you set off.
Local buses run from the main bus terminal next to the market. They are an experience in their own right: open-sided, packed, with reggae or evangelical preaching on the speakers. Most fares within Suva are under a Fijian dollar; routes are unmarked but conductors and fellow passengers are helpful. Carry small change.