I don't know how old you or your sibling are so some suggestions may not be age appropriate. I'm a Londoner and hope you have an amazing time here. There's so much to see and do it's impossible even for a resident, but here's some suggestions:
- Catch a show (or three)
West End theatre productions are world renowned and we have some of the best shows around. Some of the best ATM include Dirty Rotten Scoundrels (starring Robert Lindsay, one of Britain's most incredible actors, period), Miss Saigon (after a long time away), Book of Mormon, Wicked and The Woman in Black (very chilling!).
There are also some great comedy shows [http://www.timeout.com/london/comedy] with great names in many venues. While you're here it'll be kinda a "warm up" ahead of the Edinburgh Fringe festival in a little over a month, so there'll be tons of acts putting on tons of shows with new material.
- Get some culture
If you're an uncultured heathen, then there's plenty to to see and do to redress that! We have great galleries including the Tate, the National, the Queen's Gallery and Royal Academy of Arts. The Barbican have a cool "Digital Art [http://www.timeout.com/london/art/five-things-not-to-miss-at-digital-revolution]" exhibition on at the moment. Museums include Natural History, Science and the British Museum.
- Have a drink
There are some really cool places to grab a drink and enjoy a great atmosphere at the same time. Two standout ones include the London Stone [http://www.eerie-pubs.co.uk/london-stone] which is very gothic. They serve cocktails named for the Seven Deadly Sins and the toilets are hidden behind bookcases, proper Scooby Doo style. There's also the Seven Stars [http://www.timeout.com/london/bars-and-pubs/seven-stars] near the Royal Courts of Justice. They have a cat that wears a ruff. Avoid most sports bars, particularly now during the world cup (unless you love football). They're not bad, but not the best places to stop either.
- See some sights off the beaten path
It's easy to see the touristy stuff (you've already named some) and you definitely should. Make sure to add Buckingham Palace, Westminster Abbey, Covent Garden and Tower Bridge to the list. But there's some great stuff off the beaten path too. Someone already suggested Camden Market, a brilliant, very bourgeois, hip place. There's tons of strange shops and stalls so you might find some cool things to take home with you. While there, make sure to visit Cyberdog.
There is also the London Dungeons. They do like a "horror" themed thing about the dark side of historical London. They've done things with Jack the Ripper, the Great Fire of London and show gruesome things (all fake, I assure you). I don't know if I'd really recommend it to be honest, more just a suggestion as something to consider. The last time I took an out of town friend there, it was thoroughly tedious and uninteresting.
In quick fire mode, other options include: Carnaby Street, the East End/Brick Lane markets (on Sundays), Portobello Road (mostly antiques, but still fun) and Notting Hill.
- Take a train
Yes, you can leave London too! Trains run everywhere around the country so you could go to see Bath for a day, or Salisbury and see Stonehenge for example. You could be in Paris in < 3 hours from St. Pancras on the Eurostar so you could have a day trip/long weekend in "gay Paris" and all the amazing things there (definitely plan ahead if you're considering it).
- Shopping
There's so much shopping it's impossible to quantify. You have massive department stores like Selfridges on Oxford St., Harrods in Knightsbridge, Hamleys on Regent St., Forbidden Planet on Shaftesbury Av. and a lot more. Covent Garden has some cool little shops too.
I could write a page on each of the above, but they're just a few suggestions. Please feel free to ask anything specific and I'll be glad to help. If you tell me the exact dates you're in the city, I can tell you if there's anything special on in those times (tho in truth, you could probably google the answers as easily). If there's anything in particular you're interested in, let me know and I can go into more detail and make better suggestions.
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Other advice that you're probably aware of but I'll say anyway. London is expensive. It's not Iceland or Switzerland level expensive but not that far behind either. A starbucks coffee is about £3 or $5, a Burger King Whopper is about the same. A "travel card" to travel unlimited amounts on the Tube and buses within London is about £8 or so for a day (if bought after 9.30am). I highly recommend a travel card if you plan to make any more than two trips on London transport (irrespective of where you are going). A cinema ticket is about £10 ($16) and a theatre ticket from £15-50.
Look for a good rate for pounds at home and change your currency before you come. Don't exchange at the airport, hotel or a bureaux de change in the West End on the street,
you will get awful rates. Go into a bank if you must change here. If you don't have one already, consider getting a Visa/Mastercard which doesn't charge you for using it abroad. Don't use a bank debit card unless you want massive charges. Amex, Discover, Diner's Club are not very well supported here, but Visa and Mastercard are universally accepted everywhere.
Don't use your home mobile phone here, it will cost you a fortune. If you want to stay in touch, buy a pay as you go SIM card from any store on say EE, Vodafone or O2 with £10-£20 of credit and use that. You can stay in touch (you pay nothing for people calling you from abroad) for a fixed amount and only spend more as needed.
There are stores that sell discounted theatre/show tickets for the same day at discounted prices. These are fine and absolutely legit and you can get a fantastic deal on top tickets for premiere shows. Avoid any "ticket touts", people milling outside venues. Avoid them like the plague. Avoid "tourist trap" stores that sell fridge magnets, T-Shirts and other junk. They are overpriced and sell garbage. You can find better stuff in better stores for less.
Keep your valuables out of sight and in zip up/front pockets. Crime is not that serious a problem but there's no getting around the fact that it exists so better not to make yourself an easy target. I know it's a horrid and/or common sense thing to say but it's better to be safe than sorry. Avoid walking with smartphones out and cameras in full display, wallets in backpockets/backpacks, etc.
Generally, you would tip a taxi driver and also a waiter in a restaurant. It's discretionary but 10% is the norm for a good service, 15% if you loved it (restaurant) and cabbies whatever you fancy, though generally just round up a pound or two. Stick with black, metered cabs if you can, but for cabs only used ones which display a licence and agree on the price
beforehand. Don't trust any cabbies who tout outside nightspots or don't display a sticker like in the second picture down on this page [http://www.limeylondon.com/getting-around-london/taxi/].
Please feel free to ask anything else you wish or give more information about your interests and I will be glad to give more specific suggestions. All the best and hope you have a great time here. (Please try to leave the city in the same state as when you arrived, some of us have to live here!

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