Eton is one of England's most famous public schools, where the boys are still dressed in traditional black tail coats. There's also the option to see the Kennedy Memorial at Runnymede where King John signed Magna Carta in 1215.
Lots of places to visit for lunch - you might want to try Côte Brasserie right on the Thames - a modern, all-day French brasserie, serving regional specialities and traditional classics. Or there are plenty of traditional English pubs serving tasty snacks and meals.