We did the open buses when we went to NYC and I felt I learnt more from that, however there's no way my children would want to sit and listen. I remember doing it in Windsor as a child and I was bored. I've only seen the red ones about though tbh. Although it might be no children?
I would look at things you Want to do and see if you can group them together so you walk.
If it is just you then I would want to do
1) either the Shard or London eye. If neither of those appeal then the cable cars are a good cheap alternative but I personally find them a bit out of the way.
2) Buckingham palace, horse guard parade, Downing Street and see the changing of the guards
3) Museums, there's so many to chose from in London so it depends on your interests. Ones I've particularly liked are the science museum, natural history and the British museum.
4) for a bit of shopping people always think Oxford street etc but I think you get those shops any where so I like Camden market or Portobello Market. They're unique and have a great vibe. Oh and both have yummy food there too.
5) if neither of those appeal then Covent Garden is lovely, again unique. We usually do the theatre either before or after (before if it's an evening show or after if it a matinee) Covent Garden then we have a spot of food there, look in the cool little shops, watch all the street acts and people watch). I love Covent Garden.
If there are children then I would def do the Princess Diana Memorial Garden (get there early though as it fills up and there's limited space) and the memories fountain (you can paddle in it).