…other than Big Ben and Parliament
Go see the Tower of London. It’s slam full of interesting stuff.
It’s worth seeing. I will admit, though, that I was underwhelmed by the “gold plate” section of the Crown Jewels exhibit. I never knew the Queen’s ancestors went in for such tacky bling. On the other hand, the big diamond is stunning and beautiful.
What are your interests?
This is a city thousands of years old, with oddly-named narrow streets, historical buildings, rebuilt after a major fire and later bombings etc.
The London Eye gives great views.
The British Museum is one of my favorite places. Their collection is amazing and not to be missed.
Maybe see some theatre as well? I saw some great plays in London. Maybe go to the Globe and see what Shakespeare production they are putting on?
Pretty much everything. Also bringing my GF so any girly stuff too.
Also any good pubs or restuarants.
Went there last summer and liked:
Tower of London
Tower Bridge (many of us “yanks” don’t actually realize they are 2 different things).
London Eye. But don’t go at night unless all you want to see are “pretty lights”.
Westminster Abbey. Got to see Darwins tomb. How cool is that?
British Museum was cool.
Trafalger Square.
The “Tube”. Seriously cool for us transport-deprived Yanks. “Mind the gap” 
The play “Wicked”: absolutely the best play I have ever seen.
St. Paul’s Cathedral
Kensington Palace - cool in a “Diana lived here” kind of way.
Harrod’s Department store - nice, but couldn’t afford anything.
Pub’s on every corner. I don’t drink, but they’re great places to get a reasonably priced meal.
J.
If you do, book a seat at £15 upwards rather than take a £5 standing position at ground level. Paying the extra means you will not require medical treatment for a crick in the neck from looking up all the time.
Bear in mind also that the Globe season finishes the first week in October.
In addition to jharvey963’s ideas:
The National Museum of Science and Industry has lots of cool engines, airplanes, and sciency stuff.
The V&A Museum is also very cool.
You could consider a trip out to Kew Gardens, which is beautiful at any time, but of course not at its best in rainy autumn weather.
The museums (lots conveniently located in South Kensington) are definitely worth a visit, as noted above.
I think everyone has their list of favourite London pubs, but here’s a selection that you might consider:
The Chandos, off Trafalgar Square
Doggetts, on Southbank
Ye Olde Cheshire Cheese (yes, really!) in Fleet Street
Waxy O’Connor’s, Rupert Street, off Leicester Square
If you go to St. Pauls, go a few blocks northeast and visit the Museum of London. It’s a great place and covers everything London from prehistory on up. Between St. Pauls and MoL is Postmans Park, a very pleasant little space on the west side of St Martins Le Grand. It has memorials to ordinary people who performed extraordinary heroism.
On the Thames across from the tower of London is HMS Belfast. It’s a cruiser from WWII and now a floating museum chock full of great exhibits.
Down the Thames past Greenwhich is Woolwich Arsenal which has the **Firepower! **museum of artillery. A great place for military fans.
South of Buckingham Palace next to the Wellington Barracks is the Guards Museum. Another great military museum dedicated specifically to the five Guards regiments.
A great private museum is the Wallace Collection at Manchester Square. A well-rounded collection of art, artifacts, and yes, arms and armor. The most interesting thing about it is that the collection has not had one thing taken from or added to it. This is one of the stipulations of the founder.
I believe that if you arrange for letters of introduction from the US embassy, you can get into both houses of Parliament and watch the UK government inaction.
History?
There’s also the Imperial War Museum which is very good indeed.
Camden Market is worth a walk around but there was a fire there a while ago so I’m not exactly sure if it’s the same place that I knew.
Great pubs and food are everywhere in London IMO.
What time of year are you travelling, and what do you like to do? (Eat, drink, walk, see art, see history, see architecture?)
If you’re at all into art, you must go to the National Gallery. It’s one of my favorite places in the world. The Imperial War Museum is pretty damn cool, too.
Other than the museums, my favorites things about London are the theater and the shopping, but since you live in NYC, those will probably be less impressive to you.
Count another vote for the Imperial War Museum. The Natural History Museum is also pretty great, though there may not be much new there to you depending on where you’re from.
HMS Belfast as previously mentioned is worth a look around, though obviously it’s bit more of a specific interest than the various museums.
I would say going to a pub or two is a good plan, not just for them themselves, but to take in a bit of the scenery and perhaps some shopping. They’re easily recognisable by the groups of smokers hanging around outside moaning about the weather. 
I dunno how far away it is, but you could drive down to Portsmouth and checkout the HMS Victory.
Drive? You couldn’t sound more American if you tried 
Hour and a half by train from Waterloo to Portsmouth Harbour station
I suppose I must be biased, since I used to live there, but 20 minutes on the DLR from Bank gets you to Greenwich. It has museums (Maritime and the Old Royal Observatory), shops, several markets of varying degrees of usefulness, and a beautiful park.
Next to the Observatory, in the park, is a hill with a cool view over the city. Just look for the statue presented to London by the “People of Canada” (all of whom had a say in the matter, I’m sure, so thanks Canadians!)
If you’re feeling cheesy, get the boat back from the pier to Westminster.
I loved the Tower of London, Westminster Abbey, and the British Museum. The Tower and Westminster were a little pricey to get into, but the British Museum was free to enter and was a block from my hotel.
Keep in mind that London’s public transport is far superior to any American city’s transport (for all they bitch about it). The Tube is clean, prompt and relatively inexpensive. I haven’t taken as many buses, but they were ok-crowded (more so than the Tube). Trains to places like Portsmouth are frequent, clean and fast.
Sure, there are problems and sometimes slowdowns or cuts in service happen, but overall, compared to American public transport, you’ll think you died and went to heaven.
The Tube is very easy to use-and it’s like an amusement park ride all by itself. The first time I rode the Tube I was gawking–at the escalators that go down, down, down until you swear you’re in Middle Earth, at the ads on display–some of them quite witty and risque by American standards, at how smoothly the whole damned thing works.
End of commercial. (seriously, though, you won’t need or want a car in London).
St James Park is lovely, as are the other parks (Hyde? Regent’s? Can’t remember the names). Just walking around London is fascinating.