Hopefully I would discover one already made by a now deceased person with superpowers and a lot of negotiable currency stashed away along with a comprehensive wine cellar.
I think you need to tell us what your heros do and where they do their heroing. A bivvy tent in the local cemetry wouldn't do if you have to house a fleet of batmobiles.
I like the idea of moving around a lot so that they're not found. I like the idea of a cave or a forest, then if there's an explosion or fire or something like that, there's less chance of innocent people getting hurt. And a supermarket is a good idea.