Then make it early June like JimShoe said. Much later in June and it will be hot & humid. The combo pass for the three attractions is the best deal - did that with our two loooooong time ago.
I'll quick throw this out there - another GREAT time to go is between Christmas & New Years. All kinds of fabulous programs, many of them indoors. That area of VA is tolerable at that time of year and with a little forethought you can camp there in a 3 season rig. Williamsburg at night over the holidays is stunningly beautiful. We've done it twice and will do it again in the future. Enjoy & safe travels, no matter when you decide to go.