We'll be in London for 7.5 days. Flying in and out of Heathrow, staying probably in Mayfair area.

Here's my best guess as to what our travel patterns will be:
There will be one or two days out of town trips - for example, perhaps to Bath (Just buy tickets for this on the day of travel, no discounts available for that kind of journey I guess?)

There will be one or two days when we want to travel outside of zone 1 or 2, perhaps to Kew Gardens one day for example.

Most days we'll not need to travel before 9:30 AM, but there might be limited early morning travel (single journey on a day or to may be earlier than that). Travel to and from Heathrow will be on weekends.

We'll probably be able to make use of a few of the 2 for 1 offers that I've read are better on the travelcard versus the Oyster.

So should we get a 7 day TravelCard as the best option for us?
Is the overall cost still less for us to get a card for only zone 1 and 2?
Does that mean we have to punch out at the edge of zone 2 and then purchase a single fare card from there when we are going outside of zone 2?

Anything else we should know?