In reply to Stone_donkey: You could do Rockover, I'd tram from Picadilly to Victoria station then walk, about 20mins.
Easy bus to Manchester Climbing Centre, about 15mins. The bouldering is limited, but there are self belays, which are decent training IMO.
As others have said, The Depot bouldering is world class and well worth it if you have time. You can get a bus near to it, I'd have thought a 45min journey in total.