1) Orlando Bloom did the drama course when we were there. Famous music students there include Bryn Terfel, Jaqueline du pre and tons of others.
2) I say we because my wife did a music postgrad there at the same time but we didn’t meet until we left even though we were once on the same openday concert program together. (My composition was chosen to represent the jazz courses so I was in a group that played that - my wife won a chamber music award so she was playing later in the concert with a guitarist, but us jazzers didn’t get to see that).
3) We didn’t meet because she did early music whereas I did the jazz course and all the lessons on the jazz course were underground. You may think I am joking but literally all our lessons were in the basement except for if we had a visiting musician do a masterclass (then they used to use one of the nice airy and bright above-ground rooms, some of which have a lovely view of the lake).
4) As well as the concert hall which people have mentioned, there is a theatre and at least 2 cinemas as part of the Barbican complex. If you know where to look there are parts of the old roman wall and at least 2 ruined medieval churches. You are also not far at all from one of London’s real hidden gems, the cathedral of St Bartholomew the great, a medieval cathedral down a little side alley near Smithfield market that tons of people in London don’t even know exists. Oh and for Americans, Benjamin Franklin once worked there as a typesetter[1]
My wife now teaches at the Guildhall. It’s a pretty special place especially this time of year when it’s nice. You can go sit out by the lake in the sunshine, watch the ducks etc. It’s really peaceful even though you are yards from old street, moorgate, liverpool street etc some of the busiest parts of london.