It's Piccadilly Circus, not Square [/pedant] and it's not all that anyway. Just a busy traffic intersection with a fountain in the middle. Trafalgar Square is bigger, lots of pidgeons, Nelson's Column, National Gallery, etc.
All you need is a good map of central London and get around using the Tube - easy peasy. If you like museums head for South Kensington where the Natural History, Science, Victoria and Albert museums are all located next to each other. It's near Harrods too.
Don't bother with Belgium, spend more time in Paris.