Windmills and waterwheels are not apt.
The name comes from Babbage, who separated his design into two parts he called the mill and the store.
I’m not expert at etymology or Babbage’s work, however I strongly suspect that Babbage’s use of the word mill for part of his invention was due to its strong connotations as the ur-machine (where “ur-” means original/earliest.) And the origins of the word mill trace back to mills for grain. Thus, I’m not sure that a logo based on a windmill or a water-wheel is such a bad idea. Since wind has connotations of speed, a windmill-derived logo might be a good way to go.