I won’t advise you on where to go, Wales is a very diverse and very beautiful country, and despite living here my whole life I wouldn’t think of myself as being able to give you the best advice! I will, however, as you mentio Llandeilo, tell you about that area, as it is close to the area I grew up in, and spend quite a bit of time there.
There is still plenty of Welsh spoken in and around that area, though Llandeilo itself has become populated by many people from elsewhere, looking for houses with pretty views - but that is the state of a lot of such places in Wales. The scenery is stunning. Not far south you have one of the most impressively situated (in a scenic way) castles in… Well, anywhere! The favourite Castle of many people for its situation and views, Carreg cennen. The mountains and hills around for walking, places nearby like Brynamman (mentioned in another thread) Choosing Northern or Southern Welsh!
where the native inhabitants still mostly speak Welsh (in the South, of course, but it is all Welsh!) … Well, don’t take my word for it, because I and my family are from that area 
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