How to make a map-like view that has a custom map image?

Given the fact that you want maps functionality with custom map images and data, I would suggest looking into 3rd party SDKs that allow you to bring your own tiles. To get you started, have a look at MapBox and TileMill:

• MapBox iOS SDK — as an MKMapView alternative to display custom map tiles
• TileMill — to create custom map tiles from your game map image

I personally haven't done this before, so unfortunately I can't give you specific directions beyond this. Here's an example of using custom images as maps: http://macwright.org/2012/08/13/images-as-maps.html