What hue of footwear goes best with a dark grey shirt?

A very simple way to find the best Answer for your Question is to take a good look @ the color. Does it lean more toward Black or Brown? Gray leans more toward Black. This is simply a Safe Bet Technique, or Method. For every Rule, or in this case, Technique, there is an Exception. For example, I have seen, and have worn a Navy Blue Blazer, a white dress shirt, with blue pinstripes, Med. gray slacks, some appropriate tie [which I can't recall], a Med. brown Belt, or Cordovan {which until now, I thought was a reddish brown, but Now, am not sure}, so lets just say a reddish brown belt, and matching shoes, maybe they were Penny Loafers, it was a long time ago. I could have worn Black, which was applying the Safe Bet Rule. So Exceptions are Accepted, Occasionally Acceptable, or Excused Occasionally. Since your shirt is a dark gray, this pulls away from that Exception to the Rule application. This leaves Black as the only color shoes, or boots to wear, other than Gray, or Black, and Gray. The reason I mentioned boots is because I have a pair of Med. Gray western wear boots that I purchased in Rio Bravo, Mx. Personally, I will not wear Brown tinted, or leaning colors, such as Tan, Beige, or Khaki (this is a dull Yellowish-Brown color, and is a cloth, a very strong twilled cloth of said color). Blue will call for black shoes, and I pair Green colors with brown shoes, or boots. That's my advice & I'm staking my terrible clothing reputation on it. Next!! Take Care & Be Safe Dapper Dan{gerous}