We decided against the London City Card or whatever they call it, because mostly we wanted to see the free museums. By far the most expensive thing we did was the Tower of London, I think there was a multi-museum pass which included that and a few other sites which might be worth looking into.
A 1-2 zone pass will probably do for almost everything you're likely to do, you can always buy point to point tickets if there's something beyond the zone that you want to see. We almost always get transit passes if we're staying in a city for more than a day or two - generally they pay off within about 10 rides, and it's really easy to do that in 3 days or more. Having the pass encourages us to do things farther afield, and it's nice to have the option of hopping on a passing bus when it's hot, pouring rain or your feet hurt. And the bus routes take you past areas you wouldn't normally see in the course of sightseeing, which I think is fun. One note, though, we took a bus so we could see St. Paul's and it took nearly an hour to traverse a tiny little chunk of London - the Tube is definitely more efficient, if less scenic.