If your trip is over a weekend, as well as hitting the museums and main sightseeing spots, head for Borough Market near London Bridge station.  It's the city's oldest food market, and has a fantastic selection of food stalls at the weekend.  Then from there you can walk along the Southbank of the river Thames to get some of the best views of the city across the river - it's particularly beautiful at night.  You'll go past the Globe Theatre, the Tate Modern gallery (converted from an old power station), the Millennium Bridge (a foot bridge which you can go across to get a great view of St. Paul's Cathedral), and then get to the Southbank arts complex which has the Royal National Theatre, the Queen Elizabeth Hall and then the Royal Festival Hall (London's premier classical music venue).  This gives you a great sample of all of the oldest and newest architecture that the city has to offer, along with some of the more diverse folk to rub shoulders with along the way.