What To See & Do In London

Natural History Museum (free entry - pay for exhibitions)
If it's your first time in any big city book a bus tour with a recorded commentary so you can recognise places, learn a little history and notice new places you'd like to go back to. The ideal tour is one which lets you hop off at one or two places of interest, continue a tour for a second trip or day, and best of all combine bus and train or road and river.
An alternative is an all day or multi-day underground railway and bus ticket.
And/ or go to an area where several attractions are grouped together. Or pick one or two attractions which are your personal must sees.
Plan your day to include a famous landmark, a statue, a museum if it's iffy weather, a park if it's good weather, and the home of somebody famous or a museum on a specific interest.
A good overview would be the World's favourite London attractions which include Madame Tussaud's )(check the time for shortest queues). It is conveniently at Baker Street station beside the Planetarium.
Aim to eat in or near the museum.
For example:
1 Madam Tussaud's + Planetarium (Baker Street tube station and buses)
2 Natural History Museum (free) + Victoria and Albert Museum (Kensington area)
3 National Gallery and National Portrait Gallery (Trafalgar Square)
4 British Museum
5 Tate Gallery and Bridge
6 Tower Bridge tour and Museum of London
7 Westminster Abbey including Poets Corner
8 Houses of Parliament
9 Freud House museum or Dickens Museum
10 Children's Museum / London Zoo / Jewish Museum / cemetery tour
Sunny weather Parks - depending on your location: Regents Park combine with zoo; Green Park combine with walk along Thames or down Pall Mall to Buckingham Palace.
Outdoor shopping:
Indoor shopping: Grand - visit Harrods. Mid-price go to Selfridges. Cheap find your nearest large Primark or multi-storey Marks & Spencers. Major malls include Westfield, Brent Cross.
Out of London shopping trip - try Lakeside which has restaurants on boats. Or the one with quotations and friezes of characters.
Include one unusual eating place such as: Medieval Banquet;