Little big change I suggest here. I think GPS should have a system slightly more immersive than X/Y coordinates, like add some real (fake or invented for the lore) latitude/longitude, and reflect them on the tourist map as well. I explain what I mean with an example:

GPS showing the following:

53°13'03.3"N 23°34'49.1"E

And in the map it shows some horizontal and vertical lines (I would keep the grid too) that shows

horizontal lines: 53°13'N, 53°14'N, 53°15'N... vertical lines: 23°34E, 23°35E, 23°36E...

These separate in real life about one kilometer each, so it's viable in my opinion.

This makes it not to be so straight forward at first for a new player but once you know it, it's fast and easy to use this GPS information together with a map, apart that IMO adds lots of immersion.