I can't obviously can't list everything to do in London. To be honest sometimes it feels like there is too much to do and it's absolutely impossible to pick what and to decide how to best spend your time. For some of the popular tourist highlights see below that you should do at some point in your life. If you've done all the usual stuff then Time Out publish a 'Things to do this week' column which they update weekly and includes free things that are going on in the city. Check it out and see if there's anything that takes your fancy: www.timeout.com/london/things-to-do/things-to-do-in-london-this-week
Go up the London Eye
It definitely is a must do. Once completed you need never do it again it really is something to tick off on the old bucket list. Once you've done this one however, don't bother with any other Ferris wheel type attraction anywhere else - it's pointless. Plus, if you can afford it the dinner and champagne you can have in the pods does sound fucking fantastic!
Rent Boris Bikes
Other than walking (top choice) and public buses (joint second choice) Boris Bikes are a great way to see the city. You can get around super speedily without missing out and completely loosing your bearings like you do on the underground. There are relatively cheap with the only downsides being at busy periods you may not be able to find one and just be super careful of the frankly idiotic traffic in London - it is a frequent occurrence to witness a heated cyclist and motor vehicle driver altercation. Download the Santander Cycles App to make life easier.
Watch a performance at Shakespeare's Globe
Not the biggest Shakespeare fan, however there is something truly great about watching something written in the 16th Century and performed how it was intended and originally experienced. If you don't fancy sitting through The Merchant of Venice you can still go on tours and look around the replicate of this iconic theatre. There's also a great and authentic... burger stall in the courtyard. The bard loved his burgers.
Have a cocktail at the top of Sky Garden
Sky Garden is a complex of two restaurants and a bar at the top of 20 Fenchurch Street (Walkie Talkie building) which showcases panoramic views of the city. The setting is like your in a tropical green house surrounded by plants and trees and in the evening all lit up. It is in my opinion one of the best free things to do in London, at least it makes you feel pretty special. They do some not too pricey cocktails (for London) and so book a visit or walk-in outside of peak times to look out over this magnificent city sipping on some alcoholic crushed ice amongst some great foliage. Pure bliss.
Watch a West End show
The West End is home to a wide section of world class theatre only comparable to New York's Broadway and so you really should see something at least once. The offering is made up of long runners like The Mousetrap and Les Miserables in addition to new shows and limited runs that's come and go in the remaining theatres. Login to the Society of London Theatre to see what's on offer. Prices are generally high but shows are more frequently offering cheaper ticket options and a lot offer day seat tickets which are released each morning when the box office opens which are usually a reasonable price ranging from about £10-£20 pounds. There will likely be a little bit of a queue but don't let that put you off.
Stroll along the Southbank
There's lots of delights running along the length of the Thames and the Southbank is the cultural highlight offering all manner of things food, beverage and otherwise. You've got the Southbank Centre, BFI and National Theatre all here too adding even more but a lot of the attractions are on the streets including pop up book shops and a graffiti-ed subterranean skate park.
Experience London's free Museums
Of which there are loads. Top choices are the Victoria and Albert Museum of Art and Design - they have really great exhibitions on her which you do sometimes have to pay extra for. The Natural History Museum and Science Museum are next to each other in Kensington and both worth a visit. Another great choice is the Imperial War Museum which is obviously about Imperial War. Part of this is the Churchill War Rooms however these are at a separate location and you do need to buy tickets but worth it if you're interested as, in addition to the war rooms themselves, this lets you explore the underground command centre and a separate museum on the life of Churchill himself.
Get some down time in the Royal Parks
London is very green! Over 45% of the capital is a green space and so it would be ludicrous to visit here and not relax in one of its many parks. The Royal Parks are a good place to start with three of the main and central ones practically next to each other - Hyde, which continues on to become Kensington Gardens, Green Park, next to Buckingham Palace, and a little further down the way St James. Just north of Baker Street is Regents Park which is also home to London Zoo, walk up to the top of Primrose Hill for some of the best views of the London Skyline. You might also spots some celebs, some of the lucky ones hold residences here.
Shop - but with caution
As you can imagine you can get hold of pretty much anything in London, I'll let your mind wander as much as you like here, but their are little pockets of shops that act as shopping destinations. Want a suit head to Saville Row, Diamonds - Hatton Garden. If you're after more high street shopping though, which most ordinary folk who don't generally shop for Diamonds are, then you'll inevitably end up on Oxford Street. There is a reason it is so popular and it is a really lively street just on the edge of Soho but approach with caution as it can easily become hell on earth. Avoid Saturdays and rush hour at all costs and you'll have a splendid time. London also has two Westfield shopping centres, one in Shepherds Bush and one in Stratford so do try these if you need it all under one roof. You won't escape the crowds whatever you do though so just be prepared.
If you're brave enough to venture further into Greater London, do swing by the Royal Botanical Gardens at Kew. Kew itself is adorable and the gardens are beautiful and expansive. Ensure you have a full day to make the most of your £16 entry fee. They also have all sorts of events all year round and so do be sure to check what's coming up. Highlights include the Treetop walkway, the Palm House and the Kew Palace. http://www.kew.org/kew-gardens