You come to Eagle Point to reconnect with nature and with each other. â¢ 9,100â base elevation The city is located to the west of the Lake Mountains, which are west of Utah Lake. Travel Tips Utah.removePolicies.init(); You earned it. Find unique places to stay with local hosts in 191 countries. Eagle Mountain is a city in Utah County, Utah, United States. Things To Do Utah TravelI wanted to have some peace from the city. Popular Destinations With over 50 parks to explore, Eagle Mountain, UT has something for everyone!