There aren’t a ton of touristy things to do in Dili, but the two main things that everyone seems to visit are the statue of Jesus and the Resistance Museum.


The statue is built atop a hill, and can be seen off in the distance when you’re in Dili.
Apparently (and not surprisingly) it gets pretty busy on Sundays, but when I went on a Monday, it was fairly quiet.

Along with the huge statue, there’s a pretty good view of the surroundings.

The Resistance Museum in Dili highlights East Timor’s rough and violent road to Independence, from 1975 until 2002.
Portugal colonized East Timor in the 1700s, and was present until 1975. During the 1900s, the East Timorese started to put up a fight against the Portuguese, who then started to withdraw in 1974. By the end of 1975, the Portuguese had fully left, and East Timor declared independence, only to be invaded by Indonesia about a month later, as they were worried about having a communist state so near.
War and violence was the norm in East Timor for the next 20+ years (to the tune of 1/4 of the population being killed), and was largely ignored by the west, as they had the same feelings in regards to the possibility of a communist government.
In 1999, the UN and Indonesia came to an agreement to let East Timor vote on whether or not to remain a part of Indonesia. The vote was clearly in favor of independence, but violence continued from the pro integration party (with backing from the Indonesian military…wait, didn’t the Indonesian government agree that East Timor could vote on the issue??). Finally in 2002, East Timorese independence was formalized and they were accepted into the UN (less than 30 years after the west/UN was in favor of and supporting the exactly opposite…)
As you can probably guess, everything didn’t just change immediately over night, but they have come a long way since then. UN peacekeepers were present from the start, but were able to leave by the end of 2012.
Compared to the rest of SE Asia, it felt like there was still a very strong police/military presence, which I’m sure will be around for a while yet, but overall, it seemed to feel like a fairly safe place.

Also, an interesting little bit of info (from Wikipedia) about the name East Timor, or Timor-Leste (as it’s typically called here), or Timór Lorosa’e (in Tetum).
Timor, the name of the entire island, comes from the Indonesian and Malay word timur, which means east. Leste is Portuguese for east, and was added when they colonized the area, as it is the east side of the island. Lorosa’e means “rising sun” in Tetum and is also the word for east. So regardless of which of these names you use for the country, it essentially means East-East.