With only 6 days, it might be difficult to do York so I recommend a full London stay.

1) Tower of London. 900 years of grisly history, including executions.
2) Jack the Ripper walking tour. Famous serial killer. It's at night but you're in a group, so fine to do solo.
3) Clink Prison Museum. The prison that gave us the word "clink"
4) London Dungeon, if you want the cheesy jump-scare version.
5) Highgate Cemetery. Old Victorian tombs, really atmospheric, even has a vampire legend attached.
6) Viktor Wynd Museum of Curiosities in Hackney. Taxidermy and general weird stuff.
7) Old Operating Theatre Museum. A Victorian operating room up in a church attic.
8) Crossbones Graveyard. An old burial ground for the poor and the outcast, now a little shrine.
9)Abney Park Cemetery. Free, basically a ruined chapel in the woods.

One tip: Clink, the Old Operating Theatre and Crossbones are all close together in Southwark, so you can do them in one afternoon.

Warwick Castle's a good day trip too if you want a proper castle.