Can I suggest a Day for you? It's very touristy, but fun , it's a walk with lots of stops
Take Tube to
Tower Hill. Walk out - directly in front of you is the
Tower of London.
Stop at the Tower, or don't, it's still a cool thing to see
Walk to the Left of the Tower of London and walk across
Tower BridgeGet to the other side and turn right, walk past
City Hall and past the London Dungeons and past London Bridge Station.
Go down under the bridge and grab a bite to eat for breakfast and a Monmouth Coffee at
Borough Market (be sure to go early before the crowds go crazy).
Walk along the riverside past
Southwalk Cathedral and along Clink Street, you'll go past the
Golden Hinde and
Clink Prision Museum.
Walk parallel to the Thames and walk past
Shakespeare's Globe and the
Tate Modern. Keep following the Thames Path and go around the bend in the river, walk past the
National Theatre, Royal Festival Hall and Jubilee Gardens. You'l; also go past
Gabriel's wharf which has some little shops and stalls and the
OXO tower. You'll now be able to see
The Eye. Go on the Eye
The Aquarium and the
Saatichi Gallery are also here.
Cross Westminster Bridge (or before you go you can visit the
Florence Nightingale museum and go see
Big Ben (P.S if you're a resident of the UK you can send a letter to your MP and go up and see Big Ben for free!) and
Churchill Cabinet war Rooms if you're so inclined.
You Can then keep going and do
Westminster Abbey and Walk up
St. James Park towards
Buckingham Palace.
As you're sticking close to the river you'll get great views of St Pauls, Palace Westminster etc