Left, right and the compass (слева, справа)

On the Left, On the Right

Слева and справа are ADVERBS — they answer where? and never change their form:

Банк *слева. — The bank is on the left. Аптека справа.* — The pharmacy is on the right.

The Adjectives

Левый and правый are the matching ADJECTIVES, and they agree with their noun like any other:

Use the adverb for where something IS, the adjective for WHICH ONE.

The Four Directions

All four are masculine, and all four take на rather than в.

Being There Versus Going There

This is where the two cases you have just learned do real work. На + prepositional says where something IS; на + accusative says where it is GOING:

Наш город *на севере. — Our city is in the north. (location) Мы едем на юг.* — We are going south. (direction)

The nouns end in -е for location and keep their dictionary form for direction.