The nearest ones to the Clarion would be Peter Mark in either Merchants Quay or Winthrop St, Salon 33 next to Penneys on Patrick st, There is one called Origin in Drawbridge St just off Patrick St
Peter Mark in Cork that's where my wife almost got her ear cut off by an idiot not paying attention to his job and to make matter's worse he never apologised and charged her for the haircut. Stay away from them.
Having lived in Cork for a few years, the best hairdresser I ever found was Mike in Picasso salon - it's near Tesco on Paul Street. Lovely salon, reasonably priced and always came out with a smile.
Adore on Oliver Plunkett St. (the pedestriansied street across from the bus station) is perhaps the closest to the Clarion....it's on the right hand side coming from the Clarion and has a purple facade. I can only vouch for the beautician side of it myself which is excellent but I hear the hairdressers are v.good as well.