Ok, lemme see if I can prattle off a few ideas.
To see: Since the London Eye is a no no, how about a boat trip down the Thames? City Cruises is the one we always go on and you can buy a day ticket and ride as much as you like. It stops at Greenwich, Tower of London, Westminster and then the other side of the river at Waterloo. Also a neat way to see some of the sites.
I'd go with LisaE's version of a bus tour because the tour companies we've seen charge a whopping £20 for their tour.
Definitely check out the Original London Walks website as their walking tours are fab. If you're even remotely fascinated by the Ripper murders, their Ripper walk is a must! Plus they're very inexpensive and also very laid back.
Tower of London is always good, but can be pricey to get into and you'll spend at least a half a day there looking at everything and I'd recommend staying that long anyway just to get your money's worth.
Trafalgar Square is always good. One can sit in Trafalgar Square and soak in London with view of Big Ben in the distance. The National Gallery is right there as well which is free to get into and if you're into art, you're bound to find something there you like!
To eat: There's plenty of us here who will always heartily suggest Wagamama. Great chinese/Japanese type food. They tout as a noodle bar, but they serve lots of other stuff. www.wagamama.com will help you find one that you may be close to. There's lots of other places I could probably suggest: Food For Thought is a vegetarian place in Covent Garden that I absolutely love. Today we're meeting up with a friend and going to the World Food Cafe, another veggie place in Covent Garden. I've never been there but will let you know how it is after today!
Shopping: well, there's the usual Oxford Street. Covent Garden also a really good place to find some neat and funky shops. Me being of the Gothy persuasion, can't help but recommend Camden where there is the Camden market and the Camden lock as well as many shops along the high road. There's not just gothy stuff though. Lots of cool trendy stuff there. Good place to find great stuff!
There's also the almost obligatory trip to Harrods in Knightsbridge. There's other shops in that area as well which are nice. I don't necessarily prefer them myself. There's only a few reasons I go to Harrods anyway and Krispy Kreme is one of them! But it's also fun to just go see the bling blings and they do have some things that are geared towards tourists that are more affordable.
Ok, that's it for my suggestions at the moment! Seriously, hope you have a wonderful visit!
