The city of Aden consists of several subcities scattered around the vulcano and along the bay. The areas are Crater/Adan; Tawahi/Steamer Point; AL Ma'alla; Khormaksar; Shekh Othman; Al Shaab; and Little Aden which is at the other end of the bay on a second - smaller - vulcano. The sheraton and elephant beach hotels are at Goldmoor/Gold Mohr
If you do not have a map, it will take you some time to get a sense of orientation as most are facing the sea but all are facing a different way: after all a volcano is round.
The nicest way to get from one part to the other is a group taxi. A Japanese passenger van with the door tied open and stuffed with seats. If you raise your arm it might stop to pick you up, and if you rap against the frame it will stop to drop you off. A ride may cost you 20 to 50 ryal, depending on the distance.