I can't remember one on headrow either. I've been rummaging through images on 'leodis- a photographic archive of Leeds' but, nothing yet.
Back in late 80's we had a LBS within walking distance (probably 3 miles, like) so never ventured to town for such an outlet.
But, watson and cairns, lower briggate/junction of boar lane was the place to be! they stocked marin and, that's all I need to mention. Of course they did a comprehensive range and also did skateboard stuff. Originally they were motorbike dealers, back in 70's...
A few shops up, you find yourself on the actual juction, (where mcdonalds is on opposite corner) literally behind you is what used to be 'two wheels good' and i think it was freewheel before that, as brocklanders mentioned.
I have seen a few bike shops come and go in leeds centre, they rarely did more than 2 years. Infact, right at the top of vicar lane (opposite the old ABC cinema, now demolished) was a bike shop i can't even remember the name of.
The 'don't last' phenomenon is something i can't truly explain but, lack of parking. generic(boring) stock and upp'd prices may be in there somewhere. Stiff opposite arndale centre, headingley, had some parking at rear and failing that you could get in the streets up there, somewhere. Forget that now though! in hindsight. As the streets in headingley are largely 'resident only' etc...
Next time i'm in Drake's cycles, harehills, leeds I will ask in there, at least two remaining staff were in the industry back then, so may be wise to ask the wise. Including john Drake himself.
I'll get back if i gain any info.