The good news is that there's plenty of choice.   Wherever you are near the seaside you'll always find fish and chips being sold. 

Mr Chips

 As a family we go to Mr Chips in Pembroke Dock. When you ask, they can tell you exactly what has been in their chip oil. This means that you can safely buy chips even if someone in your family has allergies. The proprietor herself is very approachable; she has someone in the family with allergies and understands exactly how serious these can be.
They sell excellent fish and chips, and their service is normally very rapid, and the cod is always of good quality. Portion sizes and prices are very reasonable -  a 'large chips' is big enough for two!  Mr Chips is a 13 minute drive away.

Top Of The Town Chippy

If you park at Robbie's the crossing takes you to the 'Top Of The Town Chippy'. Service is a bit slow, especially as they tend to cook fish only when it's ordered, but the quality has always been good.

Robbie's, by the way, is Robertson's, the newsagent directly next to the mini roundabout at the end of Pembroke Main Street.  If you park here you don't need to go all the way round the town.

Rowlies

Rowlies, at the castle end of town next to the clock tower.  Once more, the quality is good.

Something's Cooking in Letterson

If you've been up to Fishguard then this is well-worth visiting.  It's situated on the A40 between Haverfordwest and Fishguard..  It's a standard chip shop, but it also has a restaurant where you can eat your cod, chips, and mushy peas in style.  The quality of fish and chips from both the shop and the restaurant is the very best, but it's a long way away to travel for lunch!  (44 minutes).  Incidentally, they now provide gluten-free food on a Tuesday. They are closed on Mondays.   Their website is on facebook: Something's Cooking