We have gone to Pembs every year for many years. We go for a week each September and also for the St David's Festival in May (starts 25th May this year). We used to walk the coast path all day and go to lovely concerts in the evening. neither are much of an option now as my mobility is hopeless, OH has PD and also anxiety that stops him being able to go to the concerts....BUT we hire a bungalow that looks over the sea, so can enjoy that all day, and I go to the concerts on my own, so it is still a treat.
I can only reiterate that Skomer is very beautiful and I have a wonderful photo of my two oldest DDs sitting in front of the carpets of bluebells when they were little. But no photo can capture the combination of the scent of the bluebells combined with the sea air - magic!! You do need to get to the boat as early as possible because parking runs out as do places on the boat.
All my DDs did their GCSE and A level revision on the beaches there on our May holidays.