My choice would be a mostly-underground lair. It would need a gigantic underground room with catwalks, lasers, large and heavily armed men standing guard, and probably robots. The aboveground part of it would be a large palace-like compound made of white marble, with very tall towers connected by arial walkways. The tallest tower would have an airship mooring dock and huge windows. This would all be on top of a reasonably tall mountain, tall enough to get a good view but not so tall that it's perpetually frosty.
If I were to design an entire city, I would indulge my taste for fantasy architecture. Terraces, arches, flying buttresses, arial walkways, towers, waterways/fountains, and elevated roads would play major roles. The ground would be pleasently shaded because of my tendency to build infrastructure at a lot higher than ground level. At the center of the city would be a giant tower with--this is important--a mooring dock for gigantic airships. Because I like airships. Everything that could possibly be built out of white marble or similar stone would be.
So that's what my city would be like. Not, perhaps, the most practically designed city in the world, but one that would look the coolest.