This is the Non-Catholic Cemetery in Rome (also known as the Protestant Cemetery). It's also a cat sanctuary with roughly 3 thousand cats running around at all times. It's kind of nice. It gives the place a Pet Cemetery vibe that one rarely finds outside of haunted houses and nightmares.
Honestly, it's a beautiful place that too many people miss on their trips to Rome. But the cats jumping out from behind headstones and bushes was a bit unsettling.