+1 for Pembrokeshire if not taking the bikes. Coast path is stunning, great wildlife and there are loads of nice restaurants and pubs. St Davids is lovely, as is Newport which is also handy for the Preseli hills. Some good boat trips out to the outlying islands too.
Aberaeron is also a good call – this place does great food – not stayed there though. http://www.harbour-master.com/
Gower is great too – Three Cliffs Bay, Oxwich Bay and Rhossilli / Llangennigth
Further north, Aberdyfi and the area around Mawddach estuary are also lovely but you may be frustrated if you don’t have your bike as there are some great trails locally. Some lovely spots on the LLyn and Anglesey too (I grew up on Anglesey).
To be honest you can’t go too far wrong on the coast anywhere between say Swansea and Conwy Bay. It’s all good provided you avoid the caravan shanty towns of the far north coast and the heavy industry of the SE, but even around those bits there are a few gems.