Of course some of this will depend on the weather between now and your trip, but we are expected another big storm this week, and there is already a mountain of snow up there. I would not expect Tioga Pass or Tuolumne Meadows to open much before the end of June, and maybe much later than that. You will have snow.
Look at the North Rim of Yosemite Valley for your best hiking options--that gets the most sun, and is not too high. And look at Hetch-hetchy for a lower elevation trip.
Check our our website: http://www.backpackthesierra.com/
Or just read a good mystery novel set in the Sierra; https://www.amazon.com/Danger-Falling-Rocks-Paul-Wagner/dp/0984884963