The National Gallery is one of the top free to enter tourist attractions in Britain with over 6 million visitors a year. It is open from 10am to 6pm every day and to 9pm on Fridays. it closes for a few days at Christmas and on New Years Day, otherwise it is open year round. I recommend planning your visit before you go using the website here so as not to be wandering aimlessly around vast areas that maybe you're not so keen on.
The National Gallery on Trafalgar Square - is the second most visited tourist attraction in the UK, and entry is free. It showcases European Art, I suggest you do some research before your first visit to pick out what you want to see.
The Ambassadors, 1533, Holbein - there are so many pictures here you are already familiar with and many more to discover. This one has a skull at the feet of the subjects that can only be seen from the perspective of the young man to the right.
Whistlejacket, 1762, Stubbs