Not sure exactly where this is but we go to the centre for alternative technology and have also down King Arthurs caves which i think are near to where you are. we also go to as many castles as we can (they do a good castle in Wales)
CAT is in not that near,it is in Machynlledd,which is in Powys.New Quay is lovely and generally all the beaches here are great.You can do boat trips out to see dolphins and seals with these people www.baytoremember.co.uk/ .My children are a lot smaller so I'm slightly stuck on exciting teen things,but there are intersting sights like Pentre Ifan burial chamber www.walesdirectory.co.uk/tourist-attractions/Historic_Sites_and_Archaeological_Sites/Wales9763.htm ,there are castles etc. You can hire canooes and paddle down the Teifi-very lovely. There is the Welsh woollen museum and lots of pretty towns and villages.
We often stay with Llandysul Paddlers for white water kayak courses but they also run loads of fun activities for children. There are mountain bike trails nearby apparently. If you contact them I'm sure there'll be some fun activities for your two.