Advice on Trip in the USA September

Hi, I am a European who plans to do a 2-weeks trip within the US this September. I will be in Utah doing an internship in July and August, so It is the perfect opportunity for me to make a short trip afterwards.

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I want to hear suggestions and ideas on where to go. I am not interested in doing a trip in Utah because I plan to already visit the state during my stay there. I am also willing to take a plane to any state that is not Alaska or Hawaii. Also, I do not have a driving license, so I cannot rent a car.

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Simply share ideas based on your own experience. I would really like to experience something unique I cannot experience in Europe, so feel free to suggest wieird and quirky ideas too. :). Also, I am young and open to travel by bus long distances or sleep in low quality hostels/hotels.