Yep, Oyster cards --- example of one of my fun days in London:
This was when I was out in Essex:
From within the edge of Essex, travel from zone 6 Loughton, Essex, to Russell Square, central London, to see US friends visiting London -- on my Oyster card the round trip for me was about £7.00, being a £3.50 charge each way. Tube all the way, Central Line then change for one stop on the Piccadilly.
Once there, all walked together from my friend's hotel to the British Museum -- entrance is free although donation is suggested. Had a grand time in the museum.
Walked back around to a cheap Chinese restaurant my friend knows from other visit; nothing fancy, just a mom and pop type of Chinese restaurant. Can't remember specifics but I don't remember spending more than about £10 on my own order, perhaps even a little less, including a Coca Cola and my meal. We left a tip of a couple of quid for all of us.
That day out cost me a personal total of £17 !!
I agree -- all the cool stuff down at Greenwich -- not dorky at all!