Atauro Island — the obvious day trip from Dili, an hour's run by speedboat or two by public ferry across the strait. Atauro has world-class shore diving on coral reefs that line the island's western side and a handful of low-key beach guesthouses. Easy to do as a day trip with a dive operator, but worth at least one overnight if you have the time.
Liquiçá — a small Portuguese-era town on the coast about an hour west of Dili, with a faded square, a colonial-era church, and a couple of black-sand beaches. The drive itself, on the winding coast road, is one of the more scenic in the country.
Maubisse — three hours up into the mountains, at 1,500 metres and noticeably cooler. The colonial-era pousada has a viewpoint that takes in three peaks and a valley of coffee terraces. A long day from Dili but feasible if you start early.