Learn French: Celle-ci est la meilleure destination. - This one is the best destination.

Celle-ci translates to "this one". We use the feminine form celle because it refers to the feminine noun destination. If we were talking about a masculine noun, like pays (country), we would use celui-ci.

Could I just say Celle est la meilleure destination without the -ci?

No, the demonstrative pronouns like celle or celui cannot stand completely alone. You have to add -ci to mean "this one" (closer to you) or -là to mean "that one" (further away).

Why do we use la meilleure instead of le meilleur or la mieux?

Meilleur is the adjective meaning "better" or "best" (when paired with le or la), and it must agree with the noun it describes. Since destination is feminine, we use la meilleure. You can't use la mieux because mieux is an adverb used to describe verbs, not nouns.