The Stein Stuben has apparently become a beloved family crag due to the large, flat forested area where the kids can safely play. There is also a large variety of route difficulties here and route lengths. The routes are also well-bolted so you don't have to worry about decking. There are, however, a few where a set of stoppers would be good to have with you.
The crag is in the trees, so it stays shaded when there are leaves on the trees, but gets sun in Fall and early Spring.
The crag is, as mentioned, kid-friendly, but stroller access is difficult. It's not impossible though and there is plenty of space to put it once you get it out there.

When approaching Bärnfels from Obertrubach there is a cemetary near the beginning of the town of Bärnfels. There is also a large hiker's parking lot right there. Park here. The GPS coordinates are given for this.
From here, a path leads past the left of the cemetary to the center of the town. Here you'll find a ton of hiking trails intersecting (see the picture of the post with the hiking trail signs on it). Take a right up this short, paved road to find a single track hiking trail. Follow this into the woods and after 300m you'll reach a weirdly shaped rock called the Hosenknopfstein. The approach takes 5 minutes.