Here I go again.....
Once you find the queen note which frame she is on. Next time into the hive look for her on that frame first, then work outward in each direction. With a little work the beekeeper should soon deduce that a particular queen is usually found in a certain area of the hive (3-4 frames). Mark those frames and always look for the queen there 1st, it'll save a lot of eye stress.
My mentor taught me to always look at the 3rd frame in from either side of the brood chamber (upper if double) then work toward the center followed by out to the sides. Same thing with the bottom brood chamber if she wasn't found in the upper one. The Northern District Beekeepers Association (back in the days when there was only one association between Seattle and the BC border) used to have a "Find the Queen race" every year at our annual picnic. I always won, regardless of age group. I could go into a hive and find the queen faster than any of the beekeepers who had been doing for as much as 50 years. Why? Because I listened to my mentor and I believed him.