The National Gallery is the huge building that looks out onto Trafalgar Square, Lord Nelson and his guardian lions.
This museum is truly breathtaking, in its physical size, collection names, and collection size. It covers several hundred years of important artwork and artists.
One of my favorite paintings of all time is here. It's one of da Vinci's Virgin of the Rocks. Mary and the Angel positively glow. Don't miss the huge da Vinci cartoon of Mary and Saint Anne, in a special darkened alcove just behind the Virgin of the Rocks.
Other must-see's: van Gogh Sunflowers, some Michelangelo, and some of Renoir's first pointillism studies.
Plus, the museum is open late one day each week (Wednesday last time I was there), and, being free all the time, encourages repeat visits and hours of awe-struck wanderings.