1.you want to visit Buckingham palace and try to see Queen Elizabeth the second ( Green Park tube station ).
It's very easy to get there, you just need to take the Brixton's line and stop to Victoria Station.
2. You want to relax in Hyde Park.
It's pretty close. You need to go back to Green park station and then take the line going either to Uxbridge or Heathrow and stop to Hide Park Corner.
3. You want to visit the Tower of London ( Tower Hill tube station).
From Hyde Park, it's abit more tricky to get to Tower Hill. You first need to take the tube in direction of Cockforsters and get down in Holborn and then take the line to Epping and stop down to Bank. There you need to make a change towards Monument, and the next stop will be Tower Hill.
5.You want to see Piccadilly Circus.
6. You want to go to Trafalgar Square (Charing Cross tube station).
7. You want to visit the British Museum (Holborn tube station).
8. You want to go shopping in Oxford Street ( Oxford Circus tube station)