I stayed at the Cowgate Tourist Hostel in Edinburgh, it was just one street off the Royal Mile, across from the Three Sisters pub. It was a nice place, the first hostel I stayed at in europe actually. It was really clean and it was what appeared to be converted apartments - every unit of a few rooms shared a kitchen area.
The location was great for Edinburgh being in the old city just a quick walk from the castle. Only major problem is that because it's across from the Three Sisters, it tends to get a little loud at night. No problems with safety that I could tell, just loud from all the people having a good time across the street.
I stayed at the Hatters in Manchester too, it was pretty cool and I met a ton of people there.