I was told that the internet in Djibouti CLUs was DSL. Do they give you a modem, or do you need to buy a combination modem/router?

They have an online market there on the nipr sites where you can buy/sell with other people stationed there. Generally you can get a modem dirt cheap from someone leaving.

Sir,
I recently redeployed from Camp Lemonnier a few months ago. I do believe once you purchase your internet you can use an Ethernet cable, you can ask that question to personnel who work in that office. See pic below it has the contact information.
I've included the of wireless modem I used while there. They are hard to come by because every one one wants/needs them. However, the service members leave they advertise on the local swap shop to sell them. My personal opinion, I would go with my own and if he Ethernet cable works. Sell the modem on the swap shop..
Hope this helps

Internet in Dj really like in the hooches?