London, England

Much ado has been made about London. Its history, its infamy, its royalty, its notoriety, its culture, its growth, and most recently, its expense. But don't let the headstrong British pound turn you away from visiting this cosmotpolitan wonder. Even though it is going to be more expensive than touring the US, or even Europe, you can still enjoy London without taking a major chunk out of your budget.
Accommodations are going to be the most expensive part of your trip, but there are cheap and cheerful places to be found. If you don't wish to stay in a backpackers, check out these two options: The Regent Palace hotel (excellent location, small, clean rooms, shared bath) and the no-frills and cheap but tiny as hell hotel EasyHotel, from the inexpensive EasyJet company. Following this trend of capsule-style accommodation, but with the addition of normal hotel luxuries, Japanese hotel chain Yotel will introduce its hotels to London in 2007.
If you are more up for the party scene, there are several inexpensive backpackers to be found in London. The similarly named hostelz.com and hostels.com offer a convenient way to find and book your hostel, and as both sites have a rating system, its easy to find a place thats just right for you.
Once you've found a place to rest your head and bags, experiencing London shouldn't add too much more to your money woes. Most of the museums and galleries in London are free, such as The British Museum, The National History and Science Museum, The National Maritime Museum and The Victoria and Albert Museum.
Taking a double decker bus tour around the city is an educational and inexpensive way to learn a little and to get your bearings, but buying an all-day tube pass and a free tourist guide is just as good (and cheaper to boot).
As for seeing any attractions, nightlife and theatre performances, check in with your hotel concierge. They can often tell you the cheapest places to go, give you coupons if you ask nicely, and cheap theatre seats (if you ask really, really nicely and give them a generous tip).