You might recognize this movie star rock formation from the epic opening sequence of Westworld, or on the list of top 50 climbs in North America. For me and my family we found this hike just a short drive Red Cliffs Lodge on the Colorado River near Moab.
You won't miss the Tower, there is a parking lot with a bathroom at the trailhead which leads you up a dried riverbed. The washout includes many places that would make stunning waterfalls during the flash floods but all dried up the climb is adventurous and you may even get the feeling you lost the trail a time or two.
A couple of the small stretches are fairly challenging scrambles up, and a lot of fun for us and our kids (ages 7-12). Once you pass the dried creek you'll find the trail marker to head further up.
The view only gets closer and closer, and towards the top steeper and narrower. We did get to a point where my wife felt it wasn't safe to continue but me and my oldest went ahead to the top of the giant white rock just below the tower.
TLDR: A short adventure, the dry washout would have captured most of the the fun and tower view. Keep Going up for a royal view of Castle Valley!