And how can I say: "I am swimming to Newtown" in Welsh?

I think you do because it's a name.

It's a mistake. Report it.

I try to remember it this way -If there's a a hint of meaning 'inside', it's mewn: dw i'n gweithio mewn fattri/swyddfa -I work in(side) a factory/office. Hope it helps.

"Mewn" is used before non-specific nouns eg "mewn siop" = "in a shop", or "mewn siopau" = "in shops". "Yn" is used before specific nouns eg "yn y siop" = "in the shop" and "yn y siopau" = "in the shops"

Having been a frequent visitor to Newtown, this is entirely possible.