Wednesday is your best bet.
Yes. Wednesday in early June is the quietest weekday to avoid school groups and summer crowds.
School field trips usually happen Monday or Friday so they can turn it into a long weekend. Summer vacation for most districts doesn’t start until mid-to-late June, so early June is still off-peak. Wednesday lands right in the middle of the week — families are less likely to travel midweek, and day-trippers usually don’t take Wednesday off. Tuesday is decent too, but Wednesday edges it out because Monday crowds sometimes linger through Tuesday.
If you can, aim for the second week of June. The first week still catches some late school trips, but by week two most are done.
