There aren't many interesting things to buy in Kiribati. All the clothes and consumer goods are imported anyway. But like many Pacific islands, it does a good trade in stamps. Philatelic collectors will be tempted by the rarities on offer. There are typical themes such as tropical scenes, colourful fishes and native birds etc, as well as some more unusual choices. For example, I saw a Kiribati-branded Sesame Street series! The Philatelic Bureau is also the best place to buy postcards.
What to buy: I am not a stamp collecter by any means, so more informed people would have a better idea than me about the best buys here.