Dining
Restaurant aficionados will find that eateries in general have taken a giant leap forward in the last ten years. The quantity and general quality of restaurants has improved, especially in the Nadi and Suva areas. This goes for both hotels and restaurants. Many locals with a flare for cooking have benefited from the visits of top European Chefs.
There are four basic types of cuisine in Fiji that you'll find served in homes or restaurants: `local' or Fijian, European, Chinese, and Indian. Fijian fare is more or less the same as in the rest of the South Pacific--fish, shellfish, breadfruit, dalo (taro), tavioka (cassava), pork, beef, chicken, yams, rice, lolo (coconut milk), tropical fruits such as bananas, and various greens such as taro leaves or ferns. Seasoning is mostly limited to salt, lemon juice, or hot chilies, typically applied by you after the dish is served. The best place to sample local food is in someone's home but you can also find local-stye eateries near the public markets areas in Nadi, Suva and Lautoka
Continental fare, undoubtedly influenced by the English cuisine (or lack thereof), used to be limited to that bland variety of food so many of us grew up with and don't find particularly exciting in Fiji or anywhere else - overcooked steak, potatoes and vegetables. Fortunately this has changed, at least on the restaurant scene. For example in the Nadi area the fare at the better hotels (such as the Sheraton and Regent) is certainly up to international standards. Likewise, Chefs, a restaurant, in downtown Nadi also has excellent cuisine.
If you prefer to eat what the locals eat, try any of the ubiquitous Indian restaurants. Food is inexpensive (F$3-8 per serving depending where you go) and includes curried chicken, beef, fish, crab or vegetarian fare. Meals are generally served with dahl (soup) roti (a sort of tortilla) or rice. 
Note that local Indian food is different than what you will find on the sub-continent. Perhaps because the local Indo-Fijian community has been separated from the motherland for so long, the food has evolved into a sort of hybrid or variant. However, it's still excellent.
Chinese food is also becoming more popular, and improving. One can find both Cantonese and Sezchuan style eateries in Fiji. When made with fresh, local fish and produce, the quality can be quite good. However, don't expect to find the level of sophistication you've sampled in Hong Kong or San Francisco.
Buying Groceries
Modern supermarkets and local outdoor markets feature a variety of locally grown and imported high-quality fruit, vegetables, meat, poultry and every other conceivable household item. Those used to `European vegetables' such as tomatoes, green onions, potatoes and the like need not fear they will be lost in a sea of exotic local food - there is always plenty of familiar fare to be had. Mutton, pork, chicken and beef are abundant as well. Imported, canned goods are available but tend to be expensive. There is also fine locally produced cheese, milk, eggs and other dairy products. Locally grown fruit you might enjoy include pineapples, guavas, mangos, oranges, limes, papaya avocados and bananas. If you purchase fresh fruit at the market, be sure to wash it thoroughly before eating. There are a plethora of nasty, tropical micro-organisms that may not agree with your system, so don't give them a chance to develop. Peeling the skins from vegetables and fruit is always a good idea.