Clink78 was originally a courthouse, with a few holding cells in the basement. They've converted it into a hostel & you can still stay in the holding cells if you really want to. I chose to stay in one of the dorms instead, which cost me 85 pounds for four nights (about US $140). The word "clink" apparently comes from the original jailhouse in London located on Clink Street, where it is now a museum.
The hostel still maintains some of the features of the original building, including the original layout of the courtroom, complete with plaques denoting the witness stand & the prosecutor's table. If you're feeling authoritative, you can sit in the judge's chair to check your email.
All the major tourist attractions are within walking distance of Clink78, & the hostel is just a five minute walk to Kings Cross station, where you can pick up the London Underground or a train to destinations beyond. There's even a travel shop in the hostel where you can book bike tours of the city or a day trip to Stonehenge.
One of the days I was there, I hooked up with one of my dorm mates & we walked all around the city being tourists together. It was really nice to have a travel buddy for the day, which I would have missed out on had I stayed in a hotel.