There are still plenty of shorebirds moving, plus some later warblers, cuckoos etc. But, yes, things ae certainly slowing down... But the first southbound non-breeding shorebirds will turn up in southern Ontario five weeks or so from now...
June is a great time to visit the Carden Alvar, the Bruce Peninsula, or Algonquin Park with many species in full song and relatively easy to locate. A much closer option is somewhere like Cranberry Marsh in Whitby. An early morning visit to Cranberry can be very rewarding during this time of year. I visited many times when we were living in the east end of Toronto.