It is my favourite place in the world, even when it is raining! Agree that Folly Farm is a must do - and you can spend a whole day there under cover if need be. They also do an offer where you can come back for half price or something if you're desperate! Also agree about Manorbier and Pembroke castles (there is a nice cafe in Manorbier called Beach Break), and Carew castle is good too - and there is a lovely walk around Carew tidal mill, you can go inside the mill too.
There is also the Manor House zoo (Anna Ryder Richardson's place) - we haven't been there as we always do Folly Farm - same goes for Heatherton and Oakwood but they might be worth checking out. Also the blue lagoon swimming pool at Bluestone (you don't have to be staying there to use it).
Even if it is raining, the walk through the lily pools at Bosherston to Broadhaven beach is still lovely.
Colby Woodland Garden is a fantastic national trust garden with woodland walks and they had activities like pond dipping going on when we were there earlier this summer (in the rain!) There is a cafe there too to shelter from the rain and you can walk through the gardens to a beach.
Narberth is a lovely little market town with nice shops and a great Spanish deli/tapas bar, Ultracomida. They sometimes have shows for kids and workshops in the Queens Hall there and I think there is a pottery painting place too.
There is a fab new restaurant on the beach in Tenby, the South Beach Bar & Grill, which is great for brunch/lunch.
You are bound to have at least one day of sunshine and if you do, head to Barafundle bay which is the best beach in the whole world (but don't tell everyone 
). You park at the national trust carpark at Stackpole Quay and there is the boathouse tea room there for ice creams after the walk back from the beach.
Have fun!