Big Ben is perhaps the most well-known symbol of London - it is what you see on every single keyring which is sold in almost every market stall in London. You will see A LOT of tourists around this attraction when you visit so it might be a better idea to get a London bus trip in order to make sure you visit all of the most important sites and you can get a better view than anyone else by sitting up at the top decks on the bus. If you don't want to get the bus, the London Underground is a very popular option with day travel cards from around £5-£6, it means that you can travel wherever you want, as many times as you want, plus, the London Underground is a must do when experiencing the London atmosphere. However, I would recommend that you avoid peak times when going on the London Underground as it becomes extremely busy.
The London Eye is yet another popular tourist attraction, although, this picture is kind of misleading as it looks quiet (yeah we wish.) The London Eye allows you to get some Instagram worthy pictures of London - it looks especially cool at night. You can even rent out 'pods' for special celebrations, e.g, birthdays in order to make their day extra special. The 'pods' are very spacious and allow for a maximum of twelve people along with some helpful iPads to allow you to spot famous sights. The whole way round the eye lasts around half an hour, so it is a bit slower than any fair ride.
Most importantly - the shopping. Oxford Street is quite obviously the main shopping area for tourists visiting London, but Oxford Street has high-street brands such as Topshop and NewLook. If you wanted something a little different, quirky or maybe vintage, then you are better off visiting Camden. Camden is famous for unique and cheap(er) shops and there are some really lovely restaurants in the surrounding area. Camden is the next up-and-coming hip neighbourhood, so if you want somewhere trendy and quirky, Camden would be a better place for you.
Trafalgar Square is like the centre of London. This is completely free so you can spend sometime watching the street artists and admiring the view of the fountains whilst narrowly avoiding the (far too annoying) pigeons. Trafalgar Square is always packed with people day and night, so of you're a people watcher like me, then this is the perfect venue to grab a drink and sit and watch the world go by.
There is so much more to do in London but the list is just simply never ending; Covent Garden, St Paul's Cathedral, The Shard and Madame Tussauds. Whatever you do, London will never fail to disappoint you. My best advice is to go into places which you normally wouldn't - go into a rooftop café or a quirky bar, take silly selfies with the sights, run round the London Underground not knowing whether to get the Piccadilly Line or the Victoria Line - just make sure you embrace every moment you spend there.