No stoller,it would be more difficult to get around.
There are places at the top that would be fine to bring it but you will miss all the beautiful views of Clifton Gorge or whatever it's called there. Don't miss the Yellow Spring it brings good luck if you drink from it. You might even see Dave Chappelle wondering around out there but he is more mythical kind of like Big Foot.
There are different sections of trails, up to four miles. I think it might be possible to take a stroller on a section going to the spring, but not from the main entrance, which has a steep stepped descent, and not on the side with the stream and waterfall.
A stroller is not a good idea unless you are willing to carry up steps
Strollers are highly discouraged if you are walking through the woods, but OK if you take the unpaved road. The walk can be really long if you are doing it for the first time, or very short if you know what you are doing. However, it is very pleasant.
The trails wouldn't be accessible with a stroller.
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