If you use a unit of length that is 1e33 plank lengths, and a unit of time that is 1e42 plank time, and a unit of mass that is 1e6 plank masses then big G is just 1e-9 length^3/mass*time and the speed of light is 1e9 length/time. Which would be convenient.

Along with a unit of charge that is related to the elementary charge by the square root of the fine structure constant then the conductance quantum is 1/pi units of conductance and the inverse conductance quantum is pi units of resistance. Which is somewhat funny.