London was a starting off point during the 2010 Thanksgiving holiday; although I only spent two days in the city, in reality a good feel of the city can be gotten within that time period (vs. its neighbor to the South).
Flying into Heathrow, one can catch the Underground, which painlessly goes into city center. Be sure to get an Octopus card for this trip; single-way fares are prohibitively expensive (4£ vs. 1.6£), although they may be steeper from Heathrow due to its Zone 7 allocation. Octopus is also convenient for its daily limit on use; once you reach the daily maximum (dependent on peak/non-peak travel), it stops deducting from the card. Octopus makes the world’s most expensive subway system slightly more affordable.
Transport within London was all done by a mix of Underground and buses, which are quite clearly marked (and surprisingly fast on city surface streets). It seems that nothing else is necessary to explore the city! Similarly, although I stayed at Reem Hotel (50£, recommended) in the Bayswater area, places further out of the city may be cheaper and just as convenient given the Underground’s speed. For nicer hotels, Kayak + reviews on Tripadvisor may be the way to go circa 2010.
For a short trip, walking around the Houses of Parliament, Big Ben, and Westminster Abbey in the Westminster section is a must- do. In particular, one can watch the House in session for free; if there is no line, it’s a worthwhile activity. Buckingham Palace and St. Paul’s Cathedral are underwhelming from the outside. No visit to London is complete without going to Harrod’s (although purchases may be ill-advised); also, the Tower of London was an interesting 3 hour jaunt, though it is quite expensive (18£ w/ ISIC, can get it cheaper online or using 2 for 1 coupons). On a previous trip a decade prior, I recall Greenwich, the London Aquarium, and Madame Tussauds’ being fairly interesting visits as well.
Easy connections outbound exist between London and Paris using Eurostar, though buy in advance for cheapest tickets (60-80€ o/w, cheaper r/t). Other (cheaper) ways to get there can be through Eurolines, or low-cost airfare, though beware the cost of getting to far out Luton Airport. Passing customs for France in St. Pancreas is a breeze, though don’t cross until you’ve eaten as food options in the departure lounge is limited. Also beware of the difficulty of converting pounds to euros at reasonable rates, and remember to change your quid to notes!