The_Diamond_Z

I would also add

I recently had some visitors for a week and can offer the following advice/tips.

Getting around London on the Underground/Busses is pretty easy, and you can make things even simpler by getting a Visitor Oyster Card at the Airport when you arrive. I would add about £10 of pay as you go credit which is refundable on your way out (as is the £5 deposit) but I think the card is a nice souvenir. Zone 1 & 2 will cover most things.

The River Boat idea is a great one, but I would d go for the Thames Clipper which is a commuter service but the run from the London Eye to Tower Bridge hits most of what you will want to see and recognise from a unique perspective. It is about 15 minutes and can feel like you are bobbing around more so than moving, but it is a rather nice way to get between these two top attractions (both of which I recommend). I suggest London Eye to Tower as the departure pier is easier to spot than the one at Tower. You can use the credit on your Oyster Card to pay for it, and there is no prebooking necessary so if you enjoy it - you can also return (or go further) on it. Beyond Tower or London Eye, it is just a boat ride - a nice one - but not that exciting. Also, avoid the older boats (Storm/Sky/Star Clippers). The seats just give me a back ache.

Download an app that tells you when the next bus will arrive and the where stops are. Taxis are great, but buses are also an adventure and a sunk cost on your Oyster card.

London is a sprawling city but the centre - or at least a lot of the major tourist attractions - are in a small and very walkable area. I would have a walk around this area as the first thing just to get it out of the way. By this I mean Picadilly Cirus to Leister Square to Trafalgar Square to Whitehall/10 Downing St/Big Ben/ over the bridge to the London Eye/Waterloo. Google maps will be your friend, and there are more sites to see around the area. I would come back to anything that requires going into (stores/museums/tours). Just see London by foot.

Everyone is different, but a week in one city is too much for me. Getting outside of London as a break is a good idea. Most of the big car rental firms are at St Pancras and if you do not drive into the Center of London getting around is easy with a GPS. Stonehenge is fairly popular, and if you head all the way out there, I usually do Bath/Salisbury or Warwick Castle. It is a long day but a nice day and there is a pub with surprisingly good food just around the corner (okay in the countryside this is a few miles) from Stonehenge.

We also had a day trip to Paris in the middle of the week, and it offered a nice break. If this is a once in a lifetime sort of trip then, of course, do Paris, but I would not plan to see anything that requires standing in line (the lines are always long). It is a lovely city just to walk around and experience. If you intend to visit Europe again, then I would make Paris a separate trip and if you are museum folks dedicate a day to the Louvre. What I have learned is a day is not enough, but more than one day at a time is too much.

October can be pleasant (sometimes nicer than Summer). London always has a humidity to it that means you do not get the bitter cold you experience in the desert, Chicago or New York City. To keep warm, protection from the wind is a good idea.

London is a working City with a pace and pulse. Most tourists, and there a lot of them in London do not synch up; even though everyone is polite here are a few rules to keep in mind:

What kind of things interest you on tour? I'm sure you'll get more suggestions with more info.