The London Eye is good, the lines actually move very quickly. Lots of free things to do, like visiting Hyde Park, Buck Palace, the Tate Modern, things like that. When I went to NY I did the same thing, went to the Brooklyn Bridge, Central Park etc.
Better to carry a card these days, lots of places arn't even set up for cash now (annoyingly)
Get a tube pass, that's such an easy way to get around.