"Dw i'n mynd i Aberteifi."
Translation:I am going to Cardigan.
Is Cardigan only a place over there, or can it also mean a kind of knitted button-up sweater like in the US?
Cardigan is the city where the cardigan (clothes) were initially made, with welsh wool of course. Caveat: you can't easily "go to" a sweater.
Whether or not cardigans were ever made in Cardigan (and I doubt it -- although a jeans factory did open in the town in the 1960s), the cardigan as a garment is in fact named after the 7th Earl of Cardigan, an army major general who distinguished himself in the Crimean War (1853-6) and who famously wore knitted woollen waistcoats (the sleeves were added later!).
For those of us unfamiliar with the town names in Wales, it is often difficult to write out the names when we don't know what the words are. Having said that, it is a great way to learn.
A few place names in Welsh start with the definite article, eg Y Bala
In this case the sentence is 'dw i'n mynd i'r Bala' (I'm going to Bala)
In most other cases there is no definite article in front of the name of the place, eg Aberteifi
So you don't need the 'r and the sentence is 'Dw i'n mynd i Aberteifi' (I'm going to Cardigan)
Oh ok, thanks. Is there any pattern, or are these just things that you have to remember?
As I mentioned, there aren't very many place names in Wales that start with the definite article, there isn't a pattern as far as I know.