Big fan of early July. Most years, the antler growth is far enough along to start judging their full potential, while their coats are peak orange and easy to spot. I usually end up seeing the most bucks this time of year as well, as I find them feeding in the open for longer periods. YMMV, but this has been true in my area.
August can be great as well, especially if it’s been a good moisture year and the forbs are healthy. On drier years, August is really tough for me to see as many, as I think they start to concentrate more over the limited food sources. Coats aren’t quite as orange in August either, but you can start to fully assess their score potential