Dennis,
As stated above, any time you can get on the big lake is a good time. I am almost on Cape Cod and enjoy every minute I can get out that way.
That being said. If you want to take a trip in June, I would look strongly at Oswego or Fair Haven. Your travel time would be the same and the deeper water is a lot closer to the shore.
Good luck in your decision and safe travels.
Maybe I will see you on the pike one of these days.
Richard