I've planned to make a connection between Unity and the WebGL Library Cesium. My idea for now is to export a specific part of the map from Cesium as GeoTiff-File and import it to Unity to map it on a plane.
However, I can't figure out how to do this, anyone got an idea or another solution displaying maps from Cesium in Unity?
Cesium is a consumer of maps, not a provider. Cesium's default imagery provider is Microsoft Bing, but there are also options for ESRI, OpenStreetMaps, Stamen, etc. You'll have to check the license agreements with the providers, to see if you're allowed to import their map data into your app.