Spoiler: It looks more amazing in photos, and in your imagination. But, it was still a fun outing.
The Bomarzo Monster Park in Lazio, a few hours from Rome, is supposedly where there be monsters. This article describes it quite well.
When done with all the other touristy places (what am I saying?), there will still be more places to explore near Rome. The monster park in the sacred wood, Bosco Sacro, is a place you can go wander around for a few hours. There is parking, bathrooms, and walkways. Most of the walkways are gravel and dirt and there are stairs so it is not a wheelchair friendly place.
The same architect worked on Villa D’este but this park is meant to be a fantasy world of the weird and scary.
On a bright sunny day, with children running around, this place does not seem scary. But, imagine if they opened it at night?