I live in London now (from Portland, OR). My advice:

1. Bring your laptop. You will want to be able to look up points of interests, Google maps, tfl.gov.uk (their tube and bus link - provides quickest way between two points on public transport), etc. Then, buy an adapter similar to this: UK Adapter

2. Internet: the two best places to find free internet are McDonalds (one thing they have done correctly) and libraries. Also, many cafes will provide free internet. If your hotel does not, I would suggest going to a 3G store (or a Carphone Warehouse store - they are everywhere) - buy a USB stick for 3G Mobile Broadband. It works great almost all over London - very, very useful, and I have even occasionally streamed video on it.

3. Oyster card: at any tube station buy an Oyster card. Buy it for two weeks (or however long you are going to stay) and buy it for Zones 1 and 2. There will be almost nothing outside of Zones 1 and 2 that will be of interest. This will allow you to get on any tube or bus.

4. Markets: As previous posts have mentioned, I would highly suggest visiting different markets around the city. My three favorites are: Borough Market (open Thursday, Friday, Saturday, and it has existed since 43 A.D.), the Flower Market (Sundays only), and the Sunday UpMarket (Sundays only - features awesome food and amazing clothes - usually handmade designer pieces). See this post on Yelp for it: London Markets

5. Museums: As the previous posters have said, London has amazing museums.

6. Shows: I would suggest going and seeing a show. I just saw Avenue Q, which is hilarious (and you can get tickets for 10 quid). And, the show tells you the purpose of the internet: The Internet is for...

7. Buy a guidebook with a map: I would suggest Lonely Planet's guide book for London. Having something that explains the historical significant of most places is what makes London so amazing. Also, must have maps to carry around with you - the grid system was a great invention!

8. Rent a car one day: This will cost about 100 quid (plus 30 to 50 for gas). Make sure it is automatic (it is hard enough driving on the other side of the road without having to shift with your left hand). The countryside outside of London is amazing. I would suggest visiting the Cotswolds - amazing little villages with historic castles, churches, narrow roads, brick streets, and amazing countryside: Cotswolds

9. Football: I would also highly suggest a football (soccer) match. A live match is amazing - worth whatever tickets cost. The energy is incredible.

10. Always pack an umbrella and wear shoes that can get wet. It will rain while you are out, and it is better to be prepared than soaking wet.

11. Get up early! It gets dark here at 4:30pm, so I would suggest getting up as early as possible to take advantage of the day.

Good luck! London is an awesome city, and you will have an amazing time.

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