@brighteyedgirl: I live near London, and I am a terrible, terrible person because I’ve done barely any of the touristy things lol.
The London Eye is pretty cool, as are a lot of our museums, my favourites being the Natural History museum (particularly the dinosaur bit), the British Museum (particularly the Egyptian bit), and the Science Museum. Most museums and art galleries are free of charge, though some may charge for certain areas/exhibitions.
I second checking out Covent Garden; there are some quirky shops in the area, and the street entertainers are fun to watch.
I also like Portobello Road market; again, there are some quirky stalls, plus lots of antiques, vintage clothing etc, and some great food stalls and cafes; worth a visit. Similarly, if you’re into food Borough Market is well worth checking out. I also love Camden: awesome food stalls, and loads of quirky shops, def one of my favourite places in London. Come evening they also have a good pub and music scene.
I adore Harrods as my dad works there and I’ve been many times; but it’s changed a lot 🙁 However, the Egyptian escalators and the Dianna memorial are worth a look, as are the food halls.
I’ve not been, but a lot of people like the Ice Bar near Oxford Circus (basically, a bar made of ice lol). If you want to do that though I would advise pre-booking before you come.
Afternoon tea is a pleasant, and quintessentially English, thing to do. I’ve been to both the Ritz and the Goring, and would recommend both; the Ritz was fancier, and the Goring more ‘homely’, both were lovely. Just check dress-codes as men are usually required to wear a jacket (though these can usually be rented/borrowed if necessary). Again, I would recommend pre-booking if you want to go to one of the more famous ones like the Ritz.
Check out the various shows, ballets, and operas. Lastminute.com offers tickets to popular West End shows at reduced prices, and you can get ballet and opera tickets (if that’s your thing) from as little as £25/$40 if you don’t mind sitting high up. My favourite theatres for the ballet/opera are the London Colliseum (great value) and the Royal Opera House (pricey). The Royal Albert Hall also has concerts and shows on. On a similar vein, the Globe Theatre do tours which might be of interest.
Ronnie Scott’s is a famous jazz club worth a visit. Tickets are usually about £20/$30, and drinks are pricey, but they get some top-class musicians and the atmosphere is great.
If you’re into jewellery, check out Hatton Garden; it’s chock-full of jewelery shops and prices are good (don’t forget to haggle if you buy, esp if you get more than one piece). For clothes etc, check out the Westfield malls (one is located in Stratford, the other in White City); both are shopping heaven.
My mum really rates the Tower of London, though I’ve not been. Madame Tussaud’s and the Planetarium are also popular, though personally I’m not a massive fan.
That’s all I can think of for now!