The Circle line traces its roots back to the start of the London Underground in 1863, but didn't appear as the circle line until 1949 following the nationalisation of the underground, merging the Metropolitan and District lines. This route covers by foot all the station on the original circle line (ignoring the rebranded spur extension in 2009) and is a continuous loop covering 27 stations. The route can be started anywhere, and in either direction, but I suggest starting at King's Cross St Pancras and running anti-clockwise (and thus getting the boring Euston road section out the way whilst you are not thinking and still fresh).
There are many highlights to see on the route including St Pancras station, Westminster Abbey and the lesser known Westminster Cathedral, House of Parliament / Big Ben. For added enjoyment I recommend reading the following website for some fun facts along the way, like which station is on top of plague pits, which has a diverted river over it, which has cattle ramps up from the station, where the first tube disaster occurred and which is one of two tube stations which contains all 5 vowels.