Herbs, try The Blue Ball for a lovely meal. Expect DS will love the Tudor House Museum.
Serendipity the slotties place in town is fun. You can make a quid's worth of two pees last quite a while on the cakewalks (is that what they're called?). I've strung it out by watching them to their pound then getting them to advise me when to 'fire' mine.
We always visit one of the gaudy beer gardens in town, too the Buccaneer (or the Back 'in 'ere) as our friends call it. No flash peas, absurdly huge portions. Find a table, queue up to order and pay for food, cash only.
We buy a chuckaway bbq in Sainsburys and do veggie burgers with a bonfire on South Beach and have a singalong as it gets dark one night but we're there with another family so it's easier to keep the jolly up.
There's lovely hands on museum and lots of naicer nick nack and clothes shops and caffs at Narbeth. Folly Farm really quite bearable if big for giving milk to baby goats and lots of play things.
There's a play area in the beer garden of the Carew Inn by Carew castle which are both worth a visit.
The library in Tenby is nice. You can join as a visitor and get some puter time and plenty bookage to thumb for the boy.
It is a bit dark ages, Tenby and needs sunshine.... Good luck. Meant to write this sooner but just back from Edinburgh.