I like cemeteries. Which I realize might sound kind of creepy at first, but as I think I've mentioned I'm a bit of a history buff. So I'm not hanging out in cemeteries to do anything creepy or occultish. I like roaming amongst the headstones, particularly ones that are old, and thinking about the history that is more or less buried beneath my feet.
Obviously older cemeteries are better for this kind of thing. There's a small local cemetery here in town, not very big, and while some of the stones are new, the town itself dates back to Colonial times. I think the town wasn't officially founded until after the Revolutionary War, but there's a historical marker where George Washington passed through on some sort of campaign. None of the headstones in the cemetery were quite that old. There is a marker for the town's founder, who is buried there, but it's clear he was reburied some time long after the initial internment.
Which I did not deduce from some careful historical study, but because I read it on the marker accompanying the grave site.
There are a number of stones that went back as far as the mid 19th Century, and possibly some that went even farther back but which had sadly been worn past the point where they could be read. Part of the appeal is simply knowing I'm looking at something that was put in place over a hundred years or so before I was born. I like being able to touch history, it's one of the reasons old architecture appeals to me.
Of course, the appeal of cemeteries in fiction and other media is usually based on other ideas often associated with them. Those would usually be the creepy aspects. Interestingly, most of those cemeteries all look about the same on celluloid. One of the things I have noticed in my travels is that cemeteries come in all shapes and sizes. On film, and in illustrations (with the notable exception of Mike Mignola of Hellboy fame) they all tend to follow one common layout, with the round headstones and the more spaced-out layout. This was the practice in New England and the Mid-Atlantic states, like my neck of the woods, because space and cultures allowed for it. But it's not always the case.
Asian cemeteries are much different, in part I think because they often cremate and thus have no bodies to bury and take up space. Despite another stereotype, not all Native Americans had a "burial ground." Some cultures wandered off into the woods, others made biers. And Eastern European cemeteries are just... cool. Lots of differing headstones and tombs, often with a great deal of iconography. And of course, even cemeteries around where I live are often a mix of different styles. There are no angles or cherubs in the cemetery here, but there are some obelisks and crosses, along with more traditional slabs. (Including one depicting a golf scene that looks to be from the early part of the 20th Century.)
All of which just illustrates the point that research is important if you're going to set a scene in a cemetery and have it matter what kind of cemetery they're in. Which sometimes might matter even if you don't think it does. No one's robbing graves in New Orleans with a shovel, after all.