For repairs and servicing I can recommend both Eastside Bikes and the Cadzow Place (London Road) branch of Leith Cycle Co. (formerly Sandy Gilchrist). Knowledgable, friendly, efficient and helpful.
BG Cycles in Portobello have been great too: needed an inner tube after a spate of punctures (old tyres worn out) and it was fitted for no charge which was kind and unexpected (I hadn't asked him to). Maybe they took pity as I had my son with me...