In other words where might be a natural place on Earth that would over power a compass and then some
Just about anywhere where the rocks are rich in iron. This would occur near iron ore, basalt, gabbro, and similar iron-rich rocks. You really don't need a lot of magnetite in the rock for this to move the compass needle. You don't even need magnetite - chromite or pyrrhotite rich rocks may be enough to move the compass needle off.
This is a common problem when navigating only using a compass in basalt rich areas. A good historical example is that of Tasmania. You can read about it the following article:
Magnetic rocks—their effect on compass use and navigation in Tasmania
As for a map, you're probably looking for a magnetic anomaly map.
Here's an attempt to make a global , or this one from USGS, or this one being offered for sale.