What are the makings of a good stronghold?

I've been toying with concepts of military fortresses, cities, and the like, but haven't been able to come to a consensus with myself.

Within a fantasy world, filled with magic and fantastical creatures, what have you, what traits would you give a strategic stronghold? What about these traits make them good stratagem?

One that came to mind was a fortress built into a mountain, similar to Tolkien's Erebor or Warcraft's Ironforge. Essentially two main entry/exit points, both of which are easily blocked off. The main weakness here is if the attacking force had plenty of supplies, the defending force would simply starve. Or perhaps, tunnels dug in secret (or instantly with explosive magic of some kind).