HDMI Through Hole Layout Issues
The pitch is 1.5mm and the recommended hole diameter is 0.65mm, giving you 0.85mm for two annular rings and one trace width plus two spaces. Using 0.15mm for track and space, and 0.2mm for annular ring will work. 

Those are not particularly challenging rules for PCB makers with modern equipment, particularly if you only push it to the limit in a few places (like where the tracks escape from the middle row of the connector. 

So that would be a pad diameter of 1.05mm (0.65 hole + 2 annular rings of 0.2mm).