London South Bank is always a great place for finding something to do in London on a free day. The South Bank Centre itself has always plenty going on – music concerts, art galleries, theatre plays etc, and it’s just along the riverside from the Shakespeare’s Globe Theatre as well.  They have big evening events but also do lunchtime concerts and art installations. The National Film Theatre, Royal National Theatre, Royal Festival Hall and Hayward Gallery and Queen Elizabeth Hall are clustered together in close proximity.

http://www.southbankcentre.co.uk/all-events

If you like modern art and architecture the Tate Modern is just a short walk along the wide and colourful Thames path.
http://www.tate.org.uk/

Also on the South bank of the Thames near London Bridge is Borough Market, a historic food market, which is now well known for gourmet foods. The local producers bring fresh produce for sale.  Best days are Thursday and Saturday.  You can taste everything and then buy a nice lunch to eat in the Southwark Cathedral grounds next door.  It can get very busy on Saturdays, but you certainly get a real  feel of London life there.

Right next door to that is a full size sailing replica of the Golden Hinde.

There’s a great Mediterranean restaurant at the corner of Coin Street and Gabriel’s Wharf called The Wharf where you can go upstairs and dine well with a fantastic view over the river.