If you don’t go tomorrow but are planning to go in the future, try and book up the Sky Gardens in the City. It’s free but you need to reserve a time slot which gets booked up well in advance. It does give great views looking South from the North side of the Thames and overlooks the Tower of London.
Go early and definitely the Science museum. Eating out in London is expensive but if you don’t mind Weatherspoons, they are good value. Look for 2 for 1 deals and I think the tube is free for young children but best check that before you go. Do they still do kids travel for £1 offers on Southern?