If so many famous people get a memorial at St. Paul's Cathedral, then where is Sir Christopher Wren's memorial? In the Crypt you can find a plaque stating, "If you seek a monument look around you." Yes, the Cathedral itself is a fine memorial to such an important man.
There are memorials on the cathedral floor and down in the Crypt. The Duke of Wellington has the largest memorial on the Cathedral floor, (that actually took longer to build than the whole cathedral), but you will also find Lord Nelson facing Charles Marquis Conwallis.
Whereas poets are buried at Westminster Abbey, St. Paul's Cathedral has an Artists Corner with the painters: Turner, Millais, Joshua Reynolds and Lord Leighton surrounding Wren and his family in the Crypt.
Other important names you will find in the Crypt includes: Arthur Sullivan of Gilbert and Sullivan (near the OBE Chapel), Alexander Fleming, Sir Henry Wellcome, Florence Nightingale, William Blake, Lawrence of Arabia and George Washington, as well as huge tombs and chambers for Wellington and Nelson.
Nelson's Tomb has the best spot as he was the first person of national important to be buried at St Paul's so he is under the dome. His casket though was originally made for Cardinal Wolseley but was put in storage for a few hundred years when Wolseley fell out of favour with Henry VIII when he could get him a divorce from The Pope.
The Churchill screen/gates divide the refectory and the crypt so can be seen for free when visiting the cafe/shop/toilets.
For those who choose not to climb up to the galleries, Oculus is a clever 270 degree film display where you can feel as if you are taking a tour around the cathedral.