@yellowellies, you asked about Llanelli, Burry Port and Kidwelly.
Llanelli seems to me, whenever I go there, to be quite run-down and rough. Unfortunately it's another of Wales's former industrial towns that has been ravaged by drugs and unemployment. I wouldn't choose to live in the town itself, but there are new developments out along the coast which are starting to change the feel of the area. Lots of sandy beaches for surfing and kayaking and sailing and the Beacons within easy hitting distance for hiking and cycling if you're outdoorsy.
Kidwelly and Burry Port aren't as bad but both strike me, as an English person, as quite Welsh in that a lot of the people who live there were born there, and Welsh is quite widely spoken. Carmarthenshire is, in my experience, a more Welsh-speaking area than Pembrokeshire, which is further west and was 'discovered' by the English decades ago.
I have an Engish friend who moved to Burry Port a few years ago and likes her house but doesn't feel she's been able to make many inroads into the local community, though her neighbours are pleasant. Kidwelly is nice in parts, not so nice in others. Both are starting to attract more retirees and people looking to live in a coastal situation and both are probably on a slow upward trajectory.
Ferryside, just a bit further west from Kidwelly, seems to have attracted more outsiders over the years and has a slightly more open-to-the-world feel. Ferryside and Llansteffan (on the other side of the estuary) have a lot going for them, including relatively easy access to Carmarthen which has turned from a sleepy market town into something bigger and buzzier.
I know people keep saying it but you would have to come and see these places and spend a week or two here to work out which is likely to suit you because they all have their own distinct feel. There are lovely communities and people everywhere in Wales but some places are more inward-looking than others. A lot of it comes down to you. If you're outgoing and sociable you'll find ways to connect with people wherever you go.