Take the Globe Theatre for example. Now it is true that the Globe you see before you is only a replica - it was opened by the Queen in June 1997, making it, well, not very old at all. It is also not in the right location (the original was a couple of hundred metres away from the site now). It is though, as faithful a representation of the original as is possible these days - so the experience you see when inside the Globe is almost like being there, back in the time of Shakespeare himself.
And see a play you must, as each of the plays that are performed here are 'in the round' - meaning they are performed in from of everybody in the middle of an open stage, with the people standing in balconies around the outside - just like audiences of yesteryear.
There is so much more to this place than just the performance you see though, there is also a fascinating tour, which takes place under and around the theatre itself - and aims to give a background to the theatre as it would have been in its original form in 1599.
There is also a shop, and an education centre too, which will bring you up to speed with everything related to the great bard, so why not take a little walk along the South Bank and watch as time melts before your eyes!