It depends on what level of canon you are looking for.
If you accept the Gaming books, the Death Star Technical Companion (at least one of them, I believe there were several) lists it as having both Ion drives and a series of 123 hyper-drive field generators. See chapter two, Technical Specifications.
Given that the reactor was deep inside, we could well have been seeing the ports the Ion drives used, and never realized it. In most space vehicles that we see, the source of the propulsion is visible as it's close to where it's being emitted, and we see the burning / glow / whatever -- In the Death Star, the Reactor was deep inside. I believe the Ion output ports were inside that trench along the middle.
As I recall, there is also more on this in the expanded universe; the Death Star that we eventually see was the result of a fairly substantial evolution.