I quite like St Martins In The Field.
It's a church on Trafalgar Square that has a small underground cafe, bookstore, etc set amongst old grave stones.
Also, why not a trip to a riverside pub? Try The Dove, The Blue Anchor and The Rutland.
These are all less than a 10 minute walk from Hammersmith tube station. From here, there are great walks both sides of the river going west to Barnes and beyond and east to Putney.