What to do in London

I'm coming to London next weekend (Sunday - Tuesday) and was wondering if there were any suggestions for things to do?

Obviously I'll be checking out the Shard, 20 Fenchurch etc as I've been watching them for months! I also want to do a bit of the usual tourist stuff (Madame Tussauds, Dungeon, London Eye etc...) but my girlfriend wants the usual London stuff like Buckingham Palace, Tower Bridge etc...

Are we best just getting a travel card and jumping on and off the tube all day?

Any suggestions for any nice places to eat (breakfast especially) in the Euston/Farringdon area?

Thanks!