A lot of the main tourist sites are clustered round the Westminster / Whitehall area (not all of them but many of them). This is the centre of the UK Government, the Church and Royalty.
The walk below is a walk around the area that gets you to see Houses of Parliament, Big Ben, Westminster Abbey, 10 Downing St, Cenotaph, Buckingham Palace, London Eye, Trafalgar square and more besides.
As it says on the walk "If you walked this without stopping you'd do it in an hour, but there is so much to see you probably will have done well to complete it in one day".
I think a look round this area will give you are great introduction to London and you can become a real tourist.
http://www.londontoolkit.com/walks/whitehall_walk_westminster.htm