It is a nice sail and May/June are usually the best months.
There is only one All Weather harbour on the Eastern shore of the Irish Sea on route and that is Hollyhead which has complete shelter. However make sure to avoid the headlands to the north (Carmel Head) and the South(the Stacks) on the approach, unless arriving at slack water.
I would sail down the Irish side of the Irish Sea as it is in the lea of the land from prevailing South Westerly winds and has many good harbours and marinas.
Best route would be Kip to Bangor Northern ireland. Depending on how long you have then to Ardglass marina, thence on to Howth (Dublin) then on down to Cork. This route will keep you in the relative shelter of the East coast of Ireland. I would not even consider routing via the mainland.