Bob mentions Newgale. It's a fairly sheltered west-facing beach in the northeast corner of St Brides Bay. The beach break is not too challenging so it's popular with novices.
For a bit more excitement try Freshwater West, a southwest facing exposed beach backed by high sand dunes. It has a good beach break at low water as well as point and reef breaks. But there are undertows and rips so it's not ideal for novices and you need to be a strong swimmer/paddler. There is a daily surf report on the Magic Seaweed website.
Whitesands beach (west of St Davids) is said to be good too but I've never surfed there. Try Googling it.
You can use the UKCS campsite search to find places to pitch in west Wales - there's no shortage of campsites.
Scep
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