Cut Your Teeth Crag is just before the saddle connecting Calico Basin and the section of the Calico Hills accessed from the First and Second Pullouts. From the base, there are nice views through the saddle to the big sandstone peaks, and there are even better views from the climbs themselves.
With four sport routes, two trad routes, and four or five toprope routes ranging from 5.5 to 5.8, this crag is beginner-friendly and is just a nice place to spend several hours. Because it gets a lot of sun, it is a good winter spot.
My partner and I climbed All That Jazz at Black Wall, did the walkoff to the saddle, climbed all the lead routes at the main CYT Crag, and found this kept us busy for much of the day, and it was a great one at that. I highly recommend something like that as opposed to dealing with the crowds and the lines at some of the better-known spots in Calico Basin.
Park at Red Springs and hike from there, or park legally along the road a little farther in and hike a trail starting there. The latter is shorter and more direct. Expect an approach of 20-30 minutes for most parties. The crag is on the right and almost at the saddle. The picture below is of the crag from the trail.
I have climbed the sport routes and the trad route on the main formations but none of the toprope routes. Although I have seen the anchors for some of the TR routes, what little I know about them comes mostly from the Mountain Project page.
A gully splits the crag into two distinct sections.
There are bolted anchors, but you need your own gear for toproping. Some of the TR anchors are set back enough that just using quickdraws would cause drag, rock wear, and possibly rope damage.
If it has rained recently, the rock may be too wet to climb without breaking holds and endangering yourself and ruining the climbs for others. Exactly how long to wait can be a subject of hot debate, but even the most permissive suggestions are for at least 24 hours. A general rule is that if there is standing water or the ground is damp, you shouldn't climb.
Spring, fall, winter. In summer, go very early.
None in Calico Basin. The BLM Red Rock Canyon is close by. It's not open all year and has a reservation system when it is open.