It's difficult to recommend "must sees", as my preferences will probably be different than yours. The best suggestion I can make would be to have a look at the Guidebook as there are really good descriptions there of all the major sites (along with admission costs, opening and closing times, transportation details, etc.). With good information, you can both decide what interests you the most.
Some of the sites I enjoy in London:
BA London Eye
Buckingham Palace / Changing of the Guard
Cabinet War Rooms (I'm interested in WW-II history)
Imperial War Museum
Tower of London / Crown Jewels
Musicals (check the TKTS Booth in Leicester Square for discounted tickets)
Dining in good restaurants (Santini's in the London Victoria neighborhood has great Italian food; you could also try Jamie Oliver's Fifteen Restaurant)
Tate Modern (and of course a walk across the Bridge) - it's quite extensive so will take a while to tour all the different areas.
South Bank of the Thames (seems to be quite a vibrant area at times, especially when there's a festival or other event happening)
There are LOTS of choices! With only two days, you'll have to plan well and be very selective.