It's the day, rather than the 24 hours, although the 'day' extends to 4am (not that this really helps you...)

However, given the journeys you're doing, it sounds like a PAYG Oyster card will be better, as you're only going to be doing one or two in a day (and buses may be a better bet than the Tube for some).

The only day for which I'd really recommend a travelcard over an Oyster card is when you're going to the Tower of London, and if there's more than one of you visiting. If so, then a National Rail (not Tube - although it is valid on the Tube) Travelcard will get you a very valuable 2-for-1 on entry.