I found it hard to find locations for wifi in Dili as the information was out of date. I had internet access where I stayed (which was good), but it was nice to occasionally use wifi (for updating ebooks).
Wifi options (and I only found four) included Dili Beach Hotel (about 15 minutes walk from where I was living).
This has a beach view. You were given the wifi password once you had ordered something to eat or drink. I went here a few times (it was only near the end of my time in Dili that I had time to do this). I found people were bringing laptops or tablets and it was a social way to get internet access. I had internet access where I was living, which was great, but I used wifi to update my ebooks.
Other wifi access was at the other end of the beach. There were two small businesses (one a computer shop and the other a fast food place) which had wifi.
There was a third place (below) which was also beach front, and packed. It seemed there was a high demand for free public wifi in Dili. Libraries, few as there were, were not providing wifi (and not all the libraries had internet access themselves). This place below, always had lots of people using the wifi.