We have a 12 year old girl. And she is such a great traveler. A real "go-with-the-flow". So I now that she will be happy with anything. However, she adores animals (especially dogs) and is starting to get into the "fashion scene". She is also into interesting and unique things like Guiness Book of World Records and Ripley's, etc. I had read somewhere about the horse stables at Buckingham Palace, and the possibility of seeing them and the carriages. Has anyone heard of this.

You might also want to run into Cambridge to the American Cemetary. It is about 20-30 minutes north of STN

I'm not a big fan of the "hop on, hop off" bus tours. In off season, you may find that there are long gaps between buses, and you can spend a lot of time waiting - it works better as a tour bus (for the commentary) than as a means of transportation. We found the daily tube/bus pass (cheaper after 9:30 am) works well.

I would make three priorities:
1. A play or musical one night
2. Tower of London
3. Westminster Abbey

Beyond that, fit in things according to your tastes. Rather than try to hit a bunch of museums (though there are lots of excellent ones), maybe hit someplace like Covent Garden, Oxford Street, or Harrods for the shopping experience.

The Royal Mews is where they have the royal carriages and stuff for the horses. You don't actually get to see the horses, though.

I would suggest the Tower of London, the London Eye and a bus tour for one day, and the British Museum (don't miss the Rosetta Stone or the Elgin Marbles) for the other day.

Get 1/2-price tickets to a play or musical at the TKTS booth in Leicester Square. You can get those in the morning before heading off sightseeing.

Buckingham Palace walk by and the tour of the Mews.
Tower of London
V&A Museum or British Museum

For shopping: Notting Hill and Portobello Road is close to Bayswater. Even the shops of Oxford Street woulkd be fun for a 12 year old (New Look and Top Shop)