That's a bit of a mystery. It was placed on a pike on the Hampton side of the river, but eventually disappeared. The very old story is that some secret cult stole it and fashioned it into a drinking vessel and used it for all sorts of evil things. Supposedly it's still hidden under the Raleigh Tavern in Williamsburg. Despite the fact that that area has been well excavated for research. Three of his ships sailors also came to Williamsburg and were kept in the Public Gaol until trial and hanging.

I suspect we will never know what happened to the severed head after it was, according to London Newspapers in 1719, sat on a vertical pole at the entrance of the Hampton River in Virginia for public display as a warning against other potential pirates. But, we do have legend. So here is your legend:

The Annals of Philadelphia in 1842 have a un-sourced story that says the skull was made into the bottom of a silver punch bowl and used at the Raleigh Tavern in Williamsburg. Some have taken the story farther and said this "Blackbeard's Cup" was part of a Freemason ritual. Another addition is that it's more cup shaped rather than a bowl and has the words "Deth to Spotswoode" on it (it's spelled wrong to resemble how un-standardized English writing was back then, I think).
No one has found the skull, shared it publicly, and authenticated it. A man named John Walker spent a long time in the 1990s searching for it though (and may be still looking for it). He eventually found that Edward Rowe Snow, the famous New England writer who did some work on pirate stuff, had donated his work and pirate memorabilia to the Peadody Essex Museum of Salem, MA. In that collection there was a kind of silver cup/bowl skull that Snow claimed to be Blackbeard's head, but was later shown to be a a fake - since Snow made it from getting a skull from a local biology class and coating it with silver radiator paint.

Hope that satisfies your interest in the subject. For a more detailed account of this search, see pages 203-206 of the fourth edition of Kevin Duffus's The Last Day of Black Beard the Pirate.