Mudlarking metioned - nope, you need a licence
Fairfiled Halls mentioned - yes, although they are postwar concrete they sometimes have some very good orchestral concerts, sometimes dreadful stuff as well
If you can get an evening in London - have a look at Ronnie Scotts, one of the best Jazz clubs in the known universe, and it's smaller cousin Upstairs at Ronnies.
A lot of classical concerts don't sell out so you can get tickets: Royal Opera sells months in advance but Barbican, South Bank and suchlike normally easy. LSO at the Barbican? Dvorjak on 25th, perfect antidote to a coding conference
Public transport is pretty good and all the safety scares are massively overstated by right wing agitators who want us to be afraid of our own shadows and of other people, be sensible like in any other place, its a safe city. If you hold your $1500 iphone at arms length in front of you as you exit a station someone might snatch it - just like almost anywhere.
Have a look on tfl.gov.uk website - transport for London - its really easy to use London transport and if you do travel no need for fancy tickets and apps - on the underground touch in and out with a credit card - make sure it sthe same one at each end - and it calculates the fare and caps it. On a bus you just touch in, not out as they are all standard fares
Best almost-free thing to do? Catch a bus, £2, turn on the public transport layer in google maps and find a route that goes past Westminster, St Pauls, a park or two .... etc etc. I live an hour or so north and often go in for things like galleries and music, I wonder why most tourists use the underground when for the sake of taking a little longer (OK, lots longer at some times of day) you can get an above ground top deck view of the city.
