Trip from Delaware to Utah National Parks and Grand Tetons

People from the East have a hard time visualizing the weather changes in the West with latitude and elevation. Southern Utah will be hot by June. I would go there first. The Tetons never get hot, but they get crowded in the summer.

I would take a more northerly route going across. We used to drive across the country every summer for years. There is no best route. It is good that you are going for two months. Avoid traveling more than around 300 miles in a day. Take time to stop and rest.