You did not go to Goose Neck State Park to see

the several bigbends of San Juan River?!

Since you have the picture of Mexican Hat - it is quite near the Goose Neck State Park - it is not really a park, but a big overlook for the Goose Neck - the good thing is, unlike the Horseshoe BigBend, you dont need to hike - there is a very narrow, winding road goes all the way to the overlook. The road is straightly built for this viewpoint.