There are plenty of tea rooms in Tenby offering Afternoon Tea as well as several hotels. How about the Giltar Hotel who offer delicious Traditional Cream Teas between 12 - 4pm- relan in their Cwtch lounge and enjoy deicious cream tea served against the stunning backdrop of the South Beach.
If you fancy a trip out of town why not try the Plum Tree Tea Rooms (at the Tavernspite Garden Centre) which offers Afternoon Tea with gluten free options too. Or The Potting Shed (at Manorbier Garden Centre) which offers Afternoon Tea after 2pm. And finally how about Bramleys Tea Room (in St Florence at the Grandiflora Garden Centre) who offer a Vintage Afternoon Tea package.
You can then browse the relevant garden centr at the same time! Lovely!