sorry, here i go again...i really should read everything before i start posting.
The Tube is the best way to get into London from the Airport, but its argueable that is the best way to sight see round London. An adult two zone travel card costs £7 or so, and a childs one is £2 if bought after 9.30 am.
I'd still do the hoho bus though, you will get to see most of the well known landmarks...plus, if you have time, book a 'trip' on the London Eye. needs to be booked in advance to avoid really long queues....but you can get combined London Eye/river cruise tickets.
There are also some brilliant shows on too, if the mood takes you. We saw Wicked last week, and it was

Take advantage of the weak pound, and enjoy yourself