If secret bases turn into tree houses when put in trees and caves in rocks then suuure, I'll choose secret bases. xD Because of the freedom on where it's put, and if it's changed that players can join in through wifi connection. Like what the above said, location doesn't really matter if the layout is set in stone.
But if that doesn't happen I'd choose a house/villa. Because it'd be easier to reach, and well, you could customize it and all that. It doesn't make me feel like a trainer though.. More like a daughter/son of a rich kid. ._.