Alaska, where Orthodoxy in the Americas started would be a nice starting point. There are many churches and pilgrimage sites there.
There are quiet a few monasteries here in the lower 48 also such as: St. Antony's Monastery in Florence, Arizona its like an American Mt. Athos; St. Antony's Coptic Monastery in Newberry Springs, CA; Holy Trinity Russian Monastery in Jordanville, New York; St. Pasius Serbian Women's Monastery at Mount Graham in Safford, Arizona; St. Herman of Alaska Monastery in Platina, CA; St. Thekla's Womens Monastery on the Antiochian Village campus in Bolivar, Pennsylvania. These are just a few of the most visited pilgrimage sites in the US.