Learn Italian: La cattedrale è un luogo tranquillo.

The adjective tranquillo is describing un luogo (a place), which is a masculine noun. In Italian, an adjective always matches the noun it is directly attached to, even if the main subject of the sentence is feminine.

Since this lesson is about relative superlatives, how would I change this to say 'The cathedral is the quietest place'?

You would say La cattedrale è il luogo più tranquillo. To form a relative superlative like 'the quietest', you use the definite article (il) plus più (more) plus the adjective (tranquillo).

Why does cattedrale take the feminine article la if it ends in -e?

Nouns ending in -e can be either masculine or feminine, so you have to memorize their gender. Cattedrale is feminine, so it uses la in the singular and becomes le cattedrali in the plural.

What is the plural of luogo?

The plural is i luoghi. Because luogo ends in -go, you have to add an h before the plural -i ending. This spelling rule keeps the hard 'g' sound instead of letting it soften.