The London Bridge, Borough Market and Southwark areas south of the river take a lot of exploring. In one day we would look to take in the following three things and perhaps a Tramble along the Thames Path to finish it off.
Borough Market or Mercado Metropolitano
You have two wonderful markets to pick from in this area. Borough Market is the classic, well known and established option. But further south you will come to the street eat inspired Italian Mercado which is a little edgier.
The Shard is the real centrepiece of the area and is well worth a visit. You can take in the view from the official viewpoint or grab a drink in one of the bars. More information here.
It is difficult not to fall into a tourist trap as you get closer to London Bridge but Hays Galleria is a lovely place to take in the Thames Views. There is normally always something going on at The Scoop outside City Hall too.
For something a little more cultural we would recommend taking in the White Cube exhibition space (144-152 Bermondsey St, London SE1 3TQ | Website) based in an old 70's style building. The gallery is opposite Village East (171-173 Bermondsey St, London SE1 3UW | Website) if you are looking to combine the trip with cocktails and a bite to eat.