Mary,
One day doesn't give you much time. I'd stick to Trafalgar Square and visit the National Gallery and then the National Portrait Gallery. In the National Gallery Sainsbury Wing is a good restaurant called Crivelli's Garden so you don't have to waste time looking for a place to eat.
The National Gallery website is:
http://www.nationalgallery.org.uk/
The National Portrait Gallery website is:
http://www.npg.org.uk/live/index.asp
They drive like maniacs (and on the wrong side of the road no less!) so be sure to look right when crossing the street.