My favorite city. (kinda long)
Rod Peterson -- Ormond Beach
>As Samuel Johnson said, “when you're tired of London you're tired of life…” There's more but that says most of it. On my first trip my parents and brother, who had been there before, sort of set the itinerary, but when I went there a couple of years later with my wife and kids I was better prepared from the experience and from a couple of Rick Steves' programs.
If you're flying in direct, you'll most likely arrive at around 0700 (typical transatlantic schedule), and your body will still be on stateside time. It'll be tough to stay up that first day, but try to, for the sake of the next couple of days. The bad news is you likely won't be able to get to your hotel room until the afternoon.
Get a seven day tube pass (available either at the airport, or various locations throughout the city, or through your travel agent before you leave). That gives you unlimited free tube passage, unlimited bus passage, and unlimited first tier rail service (like commuter trains to the 'burbs).
What Rick Steves recommended for the first day, particularly if you arrive on a Sunday or bank holiday when many sites are closed, was to take a boat ride from along the Strand down to Greenwich. There you'll see Cutty Sark and Gypsy Moth IV, plus a short walk gets you to Queens House, Royal Naval Museum, and the Observatory. Even if you don't do the boat ride, you can get there by the Docklands Light Railway, worth the ride by itself, and then walk under the Thames by pedestrian tunnel.
Somewhere along the way, take one of the double decker bus tours. It's not as cheesy as it might sound, because they point out a lot of things that mightn't be worth going to specifically (like the Marble Arch, although Speaker's Corner is nearby), but are worth seeing, nevertheless. There will be a couple of cheesy things, but overall it's worthwhile. And you'll likely spot a thing or two you want to go back to and investigate further. You'll also get a little perspective on how the city is laid out.
So much of London and Westminster (the twin cities, as it were) is within walking distance that you'll do a lot of walking. Even taking the tube involves lots of walking. And you might not even save any time, as some of the stations are really close together (Piccadilly Circus and Leicester Square on the Piccadilly line are only 1⁄10 of a mile apart, for example). Take a really comfortable pair of walking shoes. Do not even think about stylish. Do not use this trip to break in a pair of shoes. I was less than 50 when I went and for the first time in my life I soaked my feet at night. Trust me when I say you will walk more than you ever thought you would, and you'll do it again the next day and the next.
You will probably like to combine attractions that are reasonably close. For example, Westminster Abbey and the Houses of Parliament are right next to each other, and the Cabinet War Rooms are a half block around the corner, all just steps from the Westminster tube station. And it's a pleasant walk (down Birdcage Walk) along St. James Park to get to Buckingham Palace for the guards and also for the Royal Mews. Check the schedule for the changing of the guard. It used to be every day, but several years ago they went to every other day. Maybe they've changed it back.
Nelson Column at Trafalgar Square, and the National Gallery, are all in the Charing Cross Station area, and are a few short blocks down Whitehall from 10 Downing, Horse Guards, and the Bangueting Hall. Charing Cross is also the station which connects with the major rail lines to Kent.
Covent Garden (sort of a large flea as well as produce market) and the London Transport Museum are near the Covent Garden tube station.
Madame Tussaud's (sort of cheesy), the planetarium, and Sherlock Holmes sites are all near the Baker Street tube station. Depending on where you stay in London, you may have occasion to take the Picadilly line up to Kings Cross and then over to Baker Street for that group. One of the stops on Piccadilly is Russell Square. That's where to get off for the British Museum. You'll want to allot plenty of time there. I went for the Rosetta Stone, but there's lots, lots more.
Most of the West End theater sites are an easy walk from either Piccadilly or Leicester Square, and there's a half price kiosk at Leicester Square where you can get day-of tickets for many of the major productions for half price.
St. Paul's (don't miss the models downstairs) and the Tower, while a ways from the Westminster area sites, each have their own tube stations (St. Paul's and Tower Hill, respectively), so are easy to get to. The HMS Belfast and Tower Bridge are adjacent to the Tower, thus served by the same station. Don't miss the section of ancient Roman wall excavated just outside the station.
The Eye and the Dome weren't there when I was, so I can't help you with transportation, however the Imperial War Museum is on the south side of the Thames near Elephant & Castle station. Those and the Greenwich attractions are the few on the south bank (not that there aren't things to see).
I never got down to the Barrier, but I'd love to get a close look at it. I would think they would have some sort of museum associated with it, which would be interesting, I'll bet.
While you're there, take a taxi somewhere. London cab drivers are like no other anywhere. Unlike what you may have experienced in other cities, London cabbies are more than your average hack driver. For one thing, they have to take a test on “The Knowledge” which is roughly 12,000 streets (many of whom change names regularly throughout their course) and destinations. It takes years and a lot of dedication. And they're interesting to talk to.
You may already know that the Victory is at Portsmouth, about an hour south of London. The Mary Rose is also there, one of Henry VIII's ships which capsized in the harbor on its maiden voyage and was only raised in the last dozen or so years after spending about 500 years on the bottom.
Both times we were there, we took a day trip to drive out west. If you plan your route and manage your time it's possible to see Avebury, Glastonbury, Stonehenge, Salisbury Cathedral, and Winchester Cathedral in one day. Depending on time of year, you might be able to squeeze in Bath when you're out at Glastonbury.
There are so many other things that I'd like to see, but I don't know if or when I'll be able to get back there. And of course, I tend to like more of the historical stuff, whereas other people (such as SWMBO) quickly tire of museums.
Have fun.
Rod
Sorry that my information is about 12 or 15 years old, however that's a grain of sand compared to the 2,000 years of history in London.