the only tackle shop that i know of that is right in the city centre is Braddells, its a shop that has been there for many years and is well established. im pretty sure that it is more geared to game fishing and shooting though but they could well have a sea fishing section. worth a look!?
http://www.braddells.co.uk/index.htmlif you can drop the misses off in the town then take a quick scoot to the Belfast Angling Centre if possible, its really not far from the city centre at all
wouldnt have a clue about advising parking, soz