Only just seen this. Obv some people know it better than me but FWIW here's my impression of it from what I remember from the viewpoint of a tourist rather than a local.
Not been for about 7 years but when we went (with a 4 and 2 yo) we had a great time. We probably stayed too far out though - in the Preseli Hills. It was a great location for visiting the whole area but was half hour drive to get anywhere.
The beaches in Tenby are great. There's a choice of several and plenty of room for everyone (although it wasn't full on high season when we went - June I think as we didn't have to wait for school holidays then). Good sand for sandcastles etc and the sea is pretty safe. Probably not a lot of bodyboarding scope for the 8yo though. Bit of a walk down to the beach from the main car parks (not very far - just a long uphill with the pushchair - no worse than most places though)
As a town it's definitely more St Ives than Blackpool / Yarmouth. Probably a bit tackier than St Ives - maybe more like Cromer or Llandudno, but nothing to put you off and there's a good mix of the tasteful and the mildly tacky (I don't mind a bit of tackyness on hols anyway - wouldn't be a British seaside holiday without a bit of tat). Not quite as nice as Abersoch or Woolacombe, but more going on and vastly better than the likes of Rhyl etc.
there were a few farm type places to go to nearby, which from what I remember were pretty good for the kids.
Bosherton is lovely (although didn't go there on that holiday - that was a few year previous). Seem to remember Stack Rocks being really nice, although maybe not with a 3 and 5 yo in tow. Barafundle is also a fantastic beach, but it's a bit of a trek with kids in tow.
Some good beaches further west - can't really remember what they're called. Broad Haven or Newgale maybe? Big sandy beach near Bosherton with rockpools and a car park that isn't too far from the beach I think. Good bodyboarding / surfing as well. There was another one near there which was a lot more sheltered as well. Went there on a windy day and it was lovely and calm in the cove. Not that much use I know as I can't remember exactly where it was, but the point is that there's lots of nice beaches and we didn't have any trouble finding one that suited us whatever the wind conditions etc.
St David's is a nice place to visit as well, although not a lot for the kids. Used to be a great cafe / climbing shop (good climbing at St Davids - the rocks almost like Skye Gabbro - not that you'll be likely to be doing any climbing with the kids in tow!)
Anyway - bit hazy but hope it helps

Edit: one thing that I remember from when I was a kid was taking a boat trip out from Milford Haven to see an Oil tanker up close. Effing enormous, esp from a tiny fishing boat!
Also remember Saundersfoot from a kid, as having a really good safe beach where you could wade out a long way. Went back there on my last visit and it had gone downhill a lot (or maybe I just had rose tinted glasses about it). Wouldn't recommend bothering.
I was also on a school trip to Tenby when Bucks Fizz won Eurovision. We were allowed to stay up to watch it
