Do molecules with a hexagonal planar geometry exist?
I think it's nearly impossible to find or synthesize a "canonical" complex with hexagonal molecular geometry, but in the field of host-guest supramolecular chemistry there are numerous examples of "unusual" geometry. Probably the most well-established class of such compounds are torands ("hosts") incorporating alkali metal cations ("guests").

Check out, for example: (1) Bell, T. W.; Cragg, P. J.; Drew, M. G. B.; Firestone, A.; Kwok, D.-I. A. Angew. Chem. Int. Ed. Engl. 1992, 31 (3), 345–347, DOI 10.1002/anie.199203451.

Here is an example of the structure with potassium ion from (1), Tri-n-butyltorand-potassium picrate clathrate, which I quickly sketched in Olex2:

Top view:


Side view:


Unit cell and packing: