The hobbits meet Aragorn at The Prancing Pony in The Lord of the Rings: The Fellowship of the Ring.
The Prancing Pony is an inn in Bree, a settlement located east of the Shire. Frodo, Sam, Merry, and Pippin stop there while traveling toward Rivendell, but their stay becomes dangerous after Frodo accidentally reveals the Ring.
Aragorn is introduced at the inn under the name Strider. He warns the hobbits about the dangers surrounding their journey and agrees to guide them toward Rivendell.
The Prancing Pony is often confused with The Green Dragon, an inn in Hobbiton that appears earlier in the story. Both are Middle-earth inns, but Aragorn meets the hobbits at The Prancing Pony.