Dolphins and porpoises can frequently be seen off the Welsh Coast of Wales and the best places to spot them are off Newquay which is about an hour from Old Oak Barn on the north Cardigan coast or around St Brides Bay.
You cannot guarantee you will see them of course but there is a good chance. Dolphins are best observed on days when the sea is calm, as they are much easier to spot then. The pier at New Quay is usually a good vantage point as is anywhere along Rock Street - the closest of the New Quay Terraces to the sea.
Boat trips from Newquay can be booked from a number of companies. Mwnt is another wonderful beach where people go to see dolphins.
Again several companies including Thousand Islands offer boat trips from Whitesands Bay normally. The Ramsey waters are home to a small pod of porpoises. We ourselves have seen hundreds of dolphins over the years and it is an amazing sight - well worth the trip. The picture below is taken at The Bitches off Ramsey where it is common to see porpoises.
And from another angle taken from Ramsey looking towards St Davids!