Like others have said, we liked the London Eye and the Tower (get a ticket to the nighttime tour - it's just one small intimate group).

The first day there were did something very touristy and took an open bus tour of the city. Normally I would have thought this was a waste of time/money, but the tour guide we had was genuinely very funny and informative. I can't guarantee the other guides to the same, though.

Good luck to you. My wife and I went on a tour of Europe several years ago. We went to London, Cambridge, Paris, about seven cities in Italy, and two in Germany. London was far and away the most expensive place we visited.

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And go down to Leicester Square and try to get a last-minute ticket for one of the classic plays/shows/musicals.

Very good idea. We did that too, and got cheap tickets to a real classic: When Harry Met Sally starring Luke Perry and Alyson Hannigan.
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Matt