Personally 'Y Fenni' looks better to me, interestingly if you google 'dw i'n byw yn Y Fenni' or 'dw i'n byw yn y Fenni' it seems to be 60:40 lower case:upper case for the definite article.
That's interesting. I was referring to the more common practice of book/magazine editors, style guides, official government publications etc. Maybe the (newer?) tendency to capitalise the article is on the up though.