May is the best month of the year, period.
June, you can still have it all. Big water, evening hatch stuff is still happening, especially if you focus on northern, mountainous areas. Say, NC PA (like Pine Creek valley), or the Adirondaks are peaking. Penns will still be good. These big waters will give you the good hour at dark through June. Early June of course drakes everywhere you go. But in later June you have summer BWO spinner falls at dusk (Drunella, not Baetis variety), cahills, some sulphers left, caddis flying about, stoneflies, blue quills, and slate drakes getting going. Those waters will certainly be evening focused though and kind of die off in the heat of the day if the sun is out. Earlier day can be spent on smaller water, this is at it's peak. Dry fly fishing the mountain streams for wild brookies and browns, June is prime time, all day long. Smallmouth bass is getting going.
By July the big water evening hatch thing is certainly fading. The smaller brookie water is still good as long as flows are decent, and the smallmouth scene is peaking. By mid-month you can catch morning trico hatches on the limestoners, like Spring Creek.
August isn't the greatest fishing month, for sure. Morning trico fishing on limestoners and chasing smallies on the rivers during the rest of the day. If you get a solid rain, the small brookie streams will turn on.