Anyone who travels will think there's no place like home.

Literal

Travel do person [topic-は] anyone, hometown [like-のような] good place [topic-は] doesn't-exist [quotative-と] will-think [conjecture-だろう].

故郷のような良い所はない (there's no place as good as home) echoes the universal proverb. 誰でも (anyone) creates universal scope. だろう marks the conclusion as a confident prediction.