Cortez, United States Aneth Lodge has the best room value in Cortez. Mesa Verde National Park 10 minutes. Hovenweep National Monument 45 minutes. Indian Dances nearby. Ute Mountain Casino 11 minutes. Restaurants and city park nearby. Please be advised that if you are arriving after 10pm please inform the hotel office so we can issue you with details of your room number and key. You can cancel your booking up to 5pm on your day of arrival.