If you like walking then I would head for Anglesey. The coastal path is just so beautiful. There are many, many wonderful beaches, and many of them are unspoilt and uncrowded. I love Rhosneiger, but would also thoroughly recommend Newborough (very easy plentiful parking), Cemaes, Lligwy, Moelfre. If you like a 'traditional holiday' then Benllech is a good bet - nice fish and chip shops, but a bit busier than some of the others mentioned.
The Llyn Peninsula is also really lovely, but so crowded in the Summer that we just don't go there. You should be ok in September though.
Comwy is lovely. Llandudno has managed to keep most of it's charm despite it's size and popularity. The Great Orme is fantastic for walking and the views are incredible.
Porthmadog/ Black Rosk Sands? Morfa Bychan are more traditional seaside spots and are very nice.
Harlech and Criccieth are also really lovely and both castles are well worth a visit.
You really will be spoilt for choice with beaches and walking spots if you head to anywhere West of Llandudno/ Comwy. Sorry, but I am not a fan of the coastal spots on the North East coast.