As a West Walian, I would recommend Tenby as my favorite West Wales spot, try the buchaneer for food, plentiful and reasonable. There's a nice habour there and some boat trips. Caldy Island is worth a visit.
St Davids is also very nice, smallest city in Britain but big in character.
Both these places are beutiful and well worth going too but both are at least an hour from Cardigan.
Mwnt and Tresaith are both beautiful spots and a bit closer. See if you can see Dolphins, I remember seeing a pod when I was young, I'll never forget it.
Gareth