Thought I would share some detail that may help others deciding what to do about paying for transport in London and the 2 for 1 deal.
7-day travelcard vs. Pay as you Go
As of 2015, the new pay as you go pricing scheme [1] means that a 7-day travelcard only makes sense if you are using it for more than 5 days. Previously the conventional wisdom had the cutoff at 4 days. The 7-day Zone 1 and 2 travelcard (on oyster or paper) is £32.10. Pay as you go is capped at £6.40 a day, so 5 days or less is cheaper with Pay as you go.
Understanding the above (see [2] below), made it much easier for my wife and I to figure out how best to pay for transport during a recent 4 day visit. We determined that a combination of Pay as you Go on oyster and a one day paper travelcard gave us the best value. The only reason we did not use Pay as you go for the entire trip is because we needed the paper travelcards from National Rail to take advantage of Days Out Guide's 2 for 1 attraction offers.
What we did
On arrival at Heathrow we got another oyster card (I already had one) and put £20 on each. Each rider must have their own card. We used this for the first two days on a combo of rail and buses.
We set aside one day to be our 2 for 1 deal day. The idea here is put away the oyster and buy single day travelcards (1 for each person) in order to have the required paper ticket issued by National Rail (NOT the Underground). As far as I know you have to go to a National Rail station to get these tickets, and I think you have to buy the ticket on the day of usage. We made our way to Victoria station to get these tickets from the green National Railway machines on the street level. FYI - Depending on the time of day, the day travelcards in the machine may say they are for zones 1-2 or 1-6. Regardless you will be paying £12 per travelcard. This is a bad deal compared to £6.40 daily cap with pay as you go, but if you are using it for 2 for 1 you will likely make up for it after seeing one sight.
Important: Unlike the 7-day National Rail-issued London travelcard, you do NOT need to have a passport-sized photo to get the 1-day National Rail-issued London travelcard.
We used the 2 for 1 at Tower of London and at Churchill War Rooms. At both attractions the transaction was a smooth - we presented the travelcard tickets, an ID, our previously printed vouchers and paid the admission for one adult. The 2-for 1 saved us serious money on these two sights.
Our final day and half of transport was simply covered by adding more funds to the oyster cards. We used Underground, Busses, and Overground during our stay and was impressed with the frequency of service.
Final notes
[1] http://www.tfl.gov.uk/fares-and-payments/ticket-types/which-ticket-should-i-buy
[2] Prior to the trip, I found this information most helpful.
http://www.tripadvisor.com/Travel-g186338-c133479/London:United-Kingdom:Paper.And.Oyster.Travelcards.2.4.1.Offers.html
If you have an old Oyster card that has not been used in a couple years, you do NOT need to wait in line to have it reactivated, despite what the TFL website says. I did wait in line only to discover that all you have to do is take it to a machine and top it up.
We found that Google maps directions is fantastic at letting you figure out the best bus or rail combos on the fly all over the city.
If you have a contactless credit card you can use it like Oyster and avoid Oyster's £5 deposit. I didn't have a card like this, so I cannot vouch for it. Learn more: http://www.tfl.gov.uk/fares-and-payments/contactless