Llanddowror is no longer on the trunk road to the Irish ferry, but since the bypass opened some time ago it is just to the side. A number of seaside towns can be reached in twenty minutes; the most popular is Tenby. St. Clears is five minutes away and has a Spar and Co-op whilst the old market town of Carmarthen is ten minutes and has a wide variety of shops.
Dylan Thomas made Laugharne famous and can also be reached in ten minutes or so. Of course all these estimates assume that you have a car.