Once you find yourself in the Djibouti City, getting around is easy. Walking is a viable option in the mornings and evenings (when the temperature is bearable) and there numerous minibuses taking people around the city for next to nothing all day long.
Bus
Accessing some of the nearby towns and cities is doable by public transport. The roads are quite good and the buses are a vast improvement on the death traps that Somalia and Ethiopia use (but still old) however, due to the extreme temperatures, the buses do have a tendency to overheat and breakdown (bringing an umbrella to cover yourself from the sun is a great idea).
Four Wheel Drive
To leave Djibouti city, that’s when the problems (and costs) start to increase. As I mentioned, to visit Lake Abhe or Lac Assal you’ll need to rent a 4WD (four wheel drive) which costs in excess of $100 per vehicle + fuel. Naturally in a group of four that’s more manageable but on your own, it’s pricey.