It's not Edinburgh, and it's not city cycling, but those of you with knobbly tyres may wish to have a look at this event:
http://www.drumtochtychallenge.co.uk/
It's been going for a fair few years now, and is essentially orienteering in a Forestry Commission plantation on mountain bikes. It's five hours of hard riding with nothing more than a burger and the chance of a modest prize for the winner, but there's a good endearingly amateurish family-friendly vibe and nobody takes it too seriously.
It's on this Sunday (9th May) and they're always looking to grow, so check it out.
(PS I have no connection to the organisers other than I've been participating for probably 10 years now).