Papeete is best understood as a working harbour town that happens to be the capital of French Polynesia. The sights are limited and the city is not pretty, but a day spent on foot covers most of what there is to see: the market, the cathedral, the waterfront promenade, and a couple of museums on the western edge.
Beyond the city, the rest of Tahiti is right there: the green wedge of the Fautaua Valley rises directly behind the centre, the black-sand beaches start fifteen minutes east, and the surf break of Teahupo'o on the smaller peninsula of Tahiti Iti is an hour's drive south.