The trail isn't listed on the topo map. The Playgrounds trail is a trail probably built by rock climbers.
After parking your car, begin the hike on the trail which can be found between the bushes on the Goleta side of the road near to the telephone pole.
After a few feet you will reach a spot with yellow dirt and a jumble of ways to go. Aim right.
Follow a small gully and go into some hanging raspberry vines. Watch out for poison oak.
The trail is very well maintained for an unofficial trail. There a few spots where it may look like you have a fork in the road, but none of these turnoffs really amount to much.
You will reach the playground at a spot where there is a very large oak tree, some large boulders behind it and a fork in the road. You can take any fork. If you take the left fork, you'll go to the left side of these large boulders. If you take the middle fork you may reach the boulder and have to climb the rock and up the fallen tree to end up in a very nice little nook in the rock where it's nice to rest and have lunch in the shade. If you take the right fork, you go around the same rocks on their right and you can find your way into the same nook.
From this nook you can follow any number of faint trails that go every which way, constantly fading away and making you have to search for another trail. That's what makes this the playground. It's a place to explore. Aim at some boulders and try to make your way there. I'm sure you'll be delighted at what you find along the way.
If your goal is bouldering there are boulders everywhere. Just find one that suits you. If you're looking for the climbing rock, you'll have to find a way as far down to the bottom of this big rock formation as you can, and a little to the right.
If you want to see the Narrows, well...Let me preface this by saying that a prominent local hiking trails author and activist does not believe that anyone should be given directions to the Narrows; one must discover this place for oneself. Well, I believe he might have a point, but I think also that the problem is that there is really no way to give directions to this place. You'll just have to find it for yourself. In fact, I've had arguments with people about where it is in relation to the big rocks where you start. I'll give you one hint, and it's what we've been able to agree upon: Don't look for the Narrows in the prominent ridge of rocks to the left (looking toward Goleta.) It's more toward the right than that.
After exploring until you are exhausted, return to your car the same way you came for a total of anywhere from less than 3 miles to 4 very strenuous miles or more. And please, don't leave your bottles and cans behind.