London is definitely a must-see city. Depending on what you are used to, prices can be exceedingly high, and this can make the visit much less enjoyable. Since accommodation costs can make up a big fraction of the traveler's budget, the aim here is to get a feel of London, in as short a period as practical.
Try to get in to London in the morning. If traveling across many time-zones, try to avoid the urge to sleep your jet-lag away — this is best done in a cheaper city! At the earliest opportunity, get an Oyster card from the vending machines or from a newsstand. This will save you about half the cost of a one-way ticket on the tube and buses.
Drop your bags at the hotel, and you can start immediately. Bus tours are always a good way to get a feel of the city. The Original Tour ticket costs £26 for adults and £12.50 for children (online prices); it is a hop-on/off system, good for twenty-four hours and forty-eight hours. Three walking tours and a river cruise are thrown in. Alternatively, you can take a 4-hour walking tour with Eating London Tours. The tours include lunch and other food tastings around East London restaurants, with a mix of history about Jack the Ripper and other historical sites in East London. Tickets cost £65 for adults and include enough food to satisfy breakfast and lunch, plus a copy of the Food Lover's Guide to London.
Explore Trafalgar Square, taking the obligatory photographs. When ready, you can start the bus tour. While the bus tour allows for you to alight at any stop, I find it preferable to get an overview of the city first. The tour is short, lasting only 90 minutes. You can come back to any stop of interest either by another similar bus, or by public transportation. Unfortunately, many of the tour guides, while informative, are not quite as entertaining as those you find in New York City.
Try to arrive at the Tower of London at about 2-3 pm. Wait for one of the walking tours conducted by the Yeoman Warders, and follow the crowd as...