Certainly underground, away from prying eyes. More than likely, I'd have it near, but not underneath a major city. After all, major cities have sewage lines, subways, and other things underground that would get in the way of the construction of your fortress.
I would, however, compartmentalize everything, basically taking the same principle of space stations: Every section must be able to be quarantined at a moments notice, to to point of being able to be air-tight, or even purged. After all, you never know if your bio-weapon or genetic engineering research goes awry and you need to liquidate the results.
I would also focus on being self-reliant, in case of fund shortage, as well as reinforcement, including an exceeding amount of redundant supports, and life-support systems. Of course, I'd need to remember to keep whatever competent scientists and henchmen happy. Happy henchmen are loyal and productive henchmen.
Basically, think of a massive underground military base/laboratory, including an underground farm, geo-thermal plant, and water system, with every possible redundancy there. In a way, it'd just be an evil, underground city.
[EDIT]: Really, a good way to try and cover all the bases, pardon the pun, of keeping your base from being destroyed by your arch-nemesis, isn't to think like a villain: Its to think like the hero. What would they do to stop you?