One of my favourite places in Pembrokeshire is the National Trust Stackpole Estate
https://www.nationaltrust.org.uk/stackpole#How to get here
It’s a great place for walking and exploring with or without children and offers two of our finest beaches to walk or play on. If you’re members of the Trust you can park for free at Broadhaven South or Bosherston at their car parks. The Estate has had many owners but unfortunately the magnificent house was taken down in 1963. A few years later the Trust took over and have saved the magnificent ponds and grounds and preserved them for the public to enjoy.
Close to the Centre is the old walled garden now run by a charity who are well worth supporting – children love the crocodile and the wildflower meadows and can pick strawberries in season. The cafe is good and you can buy vegetables grown in the grounds. http://www.stackpole-walledgardens.co.uk/ 
I love to walk down to the eight arch bridge
from here and over to Stackpole Quay where
there is a toilet block and another very good National Trust cafe.
If you climb the steps from here and look back there are wonderful views of the geology that Pembrokeshire enjoys with clear lines of differing strata in the cliffs.
There’s a flat walk to Barafundle Bay which always features high up on polls for the most beautiful beach in the world. If you walk down and across the beach and up again you then have a flat walk to Broadhaven South.
There’s a choice of two routes to get there – turn left for the longer walk around the cliffs for stunning views along the coast or take the short cut across the fields and listen to skylarks soaring above you. Either route will take you to Broadhaven South beach where you can then walk up the side of the lily ponds; take the left route if you’ve parked in Bosherston or turn right to head back to the eight arch bridge and Stackpole Centre.
If you’d like to stay in the area there is a very good pub at Stackpole with rooms and good food where you’ll get a good Pembrokeshire welcome. It regularly gets very good reviews.
http://www.stackpoleinn.co.uk/
I hope you enjoy these suggestions and if you’d like to see any more photographs of Pembrokeshire please take a look at my website gallery.