If you want to give your credit card some exercise, head out to Regent Street in London City Centre. Splash some more cash at Oxford Street, Carnaby Street, and Marylebone High Street.
If you want to see a show while you're in town, try and grab some tickets at London Palladium Theatre in London City Centre. If you enjoy the show and want to see another, Piccadilly Theatre, Lyric Theatre, and Apollo Theatre are all a short walk away.