It's funny cause all my major cities are underground, cause y'know. I came from underground.
That's the dumbest idea ever. Aren't your people cold-blooded? Wouldn't you freeze in those caves? Caves are KNOWN to be notoriously cold.
Plus, if someone were to attack, all they would have to do it puncture one hole in the top of the city and simply choose from a variety of things to forget with you.
1) Set charges and cave in the whole city.
2) Dump hundreds of gallons of napalm in and then set fire to it. It would starve the caverns of oxygen and make quite a few crispy critters.
3) Fire in on everyone inside.
Not to mention that you would be extremely weakened by earthquakes.
If you are found, you most likely WILL be destroyed, and with the right infrared technology, anyone can find you.