I lived there twice (luckily for me!) for a total of 7 years. My advice is to take the Hop-on-Hop off double-decker tour FIRST. It only takes 2 or 3 hours to do the whole thing. Stay on for the first circuit and decide while on it what you want to see, then as it goes round again you can get off, see the sites and then get back on. Otherwise you will not get to see everything and it really is a great tour all on its own. If you get the chance go to Dover Castle, Leeds Castle and Blenheim Palace. I WISH I WAS GOING!

The London Library is a must see:)

Everything I can suggest at this moment in time is pretty obvious. i,e, Buckingham Place, Covent Garden, see a show in the West End ...

I'll add anything if I remember it. :)