This page has instructions for finding and climbing Wasteland Tower in southwest Hyrule.
How to Reach the Tower
You can reach the Wasteland Tower from the Kay Noh Shrine. Climb part of the way up the cliff wall south of the Kay Noh Shrine. Look for the big metal block on a wooden platform. Use Magnesis to lift the big metal block, and the platform will rise. (You might need to get rid of one or both smaller metal blocks on the platform to make it go up.)
From here, you can see a ladder on the cliff. Climb up it, then proceed along the wooden walkways and up the ladders. At the top, look around to see the tower beyond the mountains to the east. Go toward it and cross the bridges up ahead. The path will take you up some slopes and cliffs. Just look for the tower in the distance and go toward it.
How to Climb the Tower
The tower has a bog around it, but you can use Cryonis to make ice blocks on the bog. Go to the large stone that is against the south side of the tower. Climb up that stone and jump onto the tower. Then climb up to one of the platforms to catch your breath. The rest of the climb is straightforward.