London is one of my favorite cities: I make a point of going every year or two. It is always expensive. It has some of the best food in the world, especially if you stick to ethnic spots and stay away from the hotel resturaunts.
Fresh fish is great, so is the lamb: beef is unimpressive. Try the burough market (London Bridge tube stop) on Friday or Saturday morning and get some fresh diver scallops or posh bangers or literally dozens of other specialty items. From there walk along the river past the Globe Theatre to the Tate Modern. You can spend two days in the British Museum and two more in the Victoria and Albert Museum and not see everything. Most of the museums are free and are world class: During the height of the empire, the Brits got most of the good stuff and brought it home and its on display.
Everything in London is quickly accessable by tube or public transport and distances are quite short. Be sure to stop at Liberty for your girl friend when you're touring the gun shop area.
Hotel rooms are tiny and very expensive. If you want top flight, stay at the Meridian (for close to 1k a day). I stay at small hotels in the Bayswater neighborhood: still 2-300 per night for a tiny room with en suite bath, but who hangs around in a hotel when you've got the city to explore?
