Hi,
2 weeks in London itself is quite alot. If you have the time, take a 3D2N trip to Paris by Eurostar, its worth it. Buy your tickets online and you can buy now...its usually cheaper when u buy earlier. Or go up north...but will be much colder cos its Dec. Last year, London suffered one of its coldest winters ever.
London is best travelled on foot cos you do get to see alot more. What you can do is hop on one of those bus tour when you first arrive, and then return to the place you want to spend more time at the next day. Buy a day or 3 days travelcard, if not just get a zone 1-3 day pass cos you prob dont need to travel further than zone 3.
You can start from Leicester Square, then walk down to trafalgar and down pass Downing road (where the PM stays) to Big Ben (Westminster Abbey) and then you will see the London's eye. But if you are really tired, you can always take a tube..just that I personally feel being underground is a waste when you can walk. Trust me, you wont feel tired working cos its nice and cold.
Covent garden is best gone on a weekend cos there are more buskers but weekday is fine also...cos its a touristy place. Soho (a pubbing area) is okie, but be careful when you go at night...it can be quite notorious.
If you like musicals, London is the best place. Pick one you want to watch and then go buy the tickets, unless you REALLY have alot of free time they you can go to the discount booth which is at the centre of Leicester Square. This is the geniune one, the rest are not really. But those shows on sale are for THAT evening only, and usually its for the not so popular ones and you have to start QUEUING damn early. The musical must watch (in my view) is Lion King.
If you have the time, a nite Thames river cruise is also quite romantic. Do remember that during winter the sun sets at 4pm. Your days are very short, bring a tripod to take pics. (Also be careful when asking someone to take a picture for you, look around for pple who look more trustworthy or some shop person, else the fellow may just run away with ur camera when u pass it to them!!)
You can drop by Chinatown, the nearest tube station is Leicester Square (Picaddily line - Blue line) . And if you want to have chinese, go to Wong Kei, the service may nto be great but its one of the better chinese resturants that are reasonably priced. Don't try those along the main chinatown street.
Another place you must go is Towerbridge, you can take the tube or the DLR (which is the LRT version of Sg). Go there and watch the sunset...quite nice.
For shopping, its oxford street. You can walk from oxford street to bond street. Both are accessible by tube (Central Line - RED line). Bond street has more high end fashion. A most go is Selfridges, its abit like our Sg's Takashimaya. All the credit card system uses PIN, so you have to tell them that you have to sign for your transaction.
For Museums, try to go to the Mdm Tussauds...but I personally think its a waste of money . The queue is long and its usually crowded. You shld however make a trip to Natural History Museum, its free.
For food, if you are not fussy, Pub food is always more affordable. Fish n chips, stew etc. Or just pop into this franchise called "Pret-A-Manger" to get your sandwich. Its expensive by Sg standard but cheap by UK standard. Drinks are cheap from the tap. Take the opportunity to try different beers you dont get n Sg. A bottle of coke is 1.12 or min 89p, so bring WATER!
The London transport system is not the most efficient. Don't rely too much on the signal board, watch the train coming and see where its going and pay attention cos they may decide not to go that area or stop at some stops due to "signal failure". And when it says "Mind the Gap"...they REALLY mean it...the GAP is a JUMP sometimes from the train to the platform for some stations. So be careful.
You can plan your tube roads using
http://www.tfl.gov.uk/tube/
Finally december...COLD. But its quite a nice feeling when the snowflakes touches your nose. If you have not bought any winter clothes..just get a thick coat and then layer. you MUST get gloves and get those leather ones so it wont freeze as the woollen ones will if it gets wet.
Watch your belongings and wear comfy shoes. The cobbled streets had caused me to sprain my ankle twice.
Cant think of where else you can go in London. I've stayed in London for year and just returned. If you have any questions just ask. Happy to help.
Just dont ask me if I like London or not...cos working there and being a tourist is quite different.