St. James' Park
A central London park which has impressive views of Buckingham Palace to the West. It has a lake in the middle with birdlife including geese and swans; the bridge across this lake provides the some of the best views of the palace. Turn around and you will see the London Eye.
Traditionally, this has been the meeting point for fictional spies, who would choose to sit on a bench feeding the ducks and exchange a few coded phrases and their briefcases before returning to their respective Whitehall departments or foreign embassies. -- aegidian
The nearest tube is unsurprisingly St James's Park Station but you can easily walk to a number of other stations nearby including Charing Cross, Piccadilly Circus, Westminster or Victoria.
St James' Park is wedge-shaped with three well-known roads running around it - [Horse Guards Parade]?, The Mall and [Birdcage Walk]?, all of which are useful for both motor vehicles and cycles, although The Mall is closed to motor vehicles on Sundays. The Mall exits right into Trafalgar Square.
This is the closest park to Soho, just a few minutes' walk from Piccadilly Circus (walk down [Regent Street]? towards the statue at the end of Waterloo Place; the park is just down the steps and across The Mall).
At the palace end, just the other side of The Mall and the Queen Victoria Memorial is [Green Park]?. You can walk or cycle practically all the way from Westminster to Kensington or Bayswater without leaving parks - cyclists and pedestrians cross from Green Park into Hyde Park via the Wellington Arch at Hyde Park Corner.
However, officially you can only really cycle around the roads at the edge of St James's Park. It's still quite pleasant though - these are wide roads with much less traffic than other Central London roads (mostly taxis).
You can use deckchairs in the park but they're not free - sooner or later an attendant will come round much like a bus conductor. I think it's about �1.50 per chair.