I had a mega tourist day last weekend. We went to Buckingham Palace, and toured the State Rooms which are open to the public during the summer. We also went to the Queen's Gallery (which houses her private collection of art), and to the Royal mews to see the horses and carriages. It was such a good day! The State rooms are amazing. You go in through the Ambassadors Entrance, and through all the sitting rooms, ballroom, dining rooms, and reception rooms. Absolutely stunning. Everything you look at is gold, or edged in gold, but it's very regal.
When you exit the palace, you come out at the back, and walk out through the gardens. You would never know that you're in central London: see the pictures above.