In reply to gazfellows:
Mother Carey's is my favourite crag in Pembroke. It's pretty accessible, has great routes, stuff you can do at various states of tide and is very beautiful. It's not really an introduction to sea cliffs though, it's pretty full-on in terms of getting the tides right (it comes in very fast there!) and climbing in an intimidating setting. But jumping in the deep end can be fun and rewarding!
The most popular place to start is St Govans, because it's most accessible: non-tidal and not much trouble from the army. It does have good routes and it's convenient, but it's a bit like climbing in a big quarry and many of the routes are horribly polished. It's pretty shit compared to Pembroke at its best.
You'll find that the tides and army will dictate where you climb. If you want a gentle intro and you've got access to the Range, starting at somewhere like Stennis is a common starting point: easy scramble access, non-tidal, brilliant (but very popular) E1s. A bit further into the Range and you've just got bags and bags of quality: Bosherston, the Leap, and all the rest of it. Just get on the classic routes that are in the sun, and not underwater. Real "must do's" in the Range around E1/2 include
Lucky Strike (E1 5b),
Keelhaul (E2 5c),
Manzoku (E1 5b),
The Beast from the Undergrowth (E2 5b),
Wishful Thinking (E1 5b) but all the classics are brilliant and live up to the hype.
Word of warning: beware of smeg. I've never quite understood it, but big seas and overcast, humid days will coat the rock in slippery slime and will add extra grades onto everything. Don't bother getting up early, the crags will be smeggy first thing.
It's some of the best climbing in the UK, have a great time.
Post edited at 12:18