Go through the list of CTs to detect all relevant geometric categories. One way of sorting the CTs (other than the heading in this RG) is to sort them by domain category. That would be interesting as well! I wouldn’t have to go through all the list again, just work from the RG and maybe modify a little.
Topology: Simplicial complexes, CW complexes, simplicial sets, etc, etc.
Differential geometry, PL stuff, structure groups.
Complex geometry, almost complex structures.
Schemes. Overview of the most important base schemes and important categories based on smoothness and properness conditions and maybe other absolute or relative conditions.
Algebraic spaces and stacks.
Various notions of derived algebraic geometry.
At least 5 different variants on rigid analytic spaces.
Interuniversal geometry.
Algebraic objects.
Tropical geometry??
nLab page on B30 Geometric categories