If not Conwy then maybe Bangor?
Further...
If Conwy is close, how about Deganwy?
Closer...
Bingo!
Llandudno, or St George's Bay, was put forward as a port that was nearer to Dublin than Liverpool, but didn't involve devising railway bridges over the Conwy and the Menai Straits (a feat that Telford had done just decades earlier for horse and cart). Detractors pointed out that if boats from Dublin were expected to sail past Holyhead, why should they stop at the Orme rather than carry on to Liverpool?
(Having failed to get Parliamentary support for transforming the Llandudno area into an industrial hub, the local landowners decided to develop it as a resort instead.)
So along with Holyhead and Porth Dinlleyn, we have three of the four. (Porth Dinlleyn was the port of choice for Charles Vignoles, who surveyed a route through mid-Wales and along Cardigan Bay. He was supported by landowner William Maddocks, of Porthmadog fame.)
The remaining port was Brunel's suggestion for a route to Dublin, but based off his Great Western Railway route. When he lost out to Holyhead, Brunel turned his attention to Neyland and the transatlantic market instead. But where did he have in mind beforehand?