Fishguard is about the only anchorage in Cardigan Bay accessible at all states of the tide. Tides are approximately Milford Haven + 0115; see Weather and Tides.
Lower Town harbour dries, but is usually accessible HW +/- 3. It’s managed by Pembrokeshire County Council and the Harbour Master is Paul Butler (07812 559482). Visiting yachts can dry out against the quay if there’s room.
The commercial port in Goodwick is managed by Stena Line Ports Ltd and discourages yachts. Their website is fishguardport.co.uk