The Recoleta Cemetery is not just any cemetery, it's a walled city of the dead housing the remains of everyone who's been anyone in Argentina's history. Eva Perón is the most famous "resident" but you'll find past presidents and military figures.
There are over 4,000 above-ground vaults and each is private property that belongs to the family. They are responsible for maintaining the space and that's why you'll see many that appear abandoned. Likely there is no one left to care for it.
Visiting is no longer free for tourists so bring your credit card to pay the entry fee, it's definitely worth it. If you have the time, I highly recommend hiring a tour guide to get more out of your visit here. There is a wealth of history and lore here (even ghost stories, it IS the city of the dead after all!).
TIP: There isn't much shade here, if you visit in the hot summer months then avoid visiting in midday. Go for early morning or before they close in the afternoon.