My all-time favourite game is the original Grandia. I like it for its wonderful blend of light-hearted comedy and a strong, compelling narrative. Grandia is one big adventure, to the point that main man Justin actually refers to the journey as an adventure - which, indeed, is his only real incentive to leave home in the first place. His optimistic, high-spirited nature will very likely remind a modern audience of Finn the Human from Adventure Time. It should also be noted that Grandia's innovative and intuitive combat system is hailed as a work of genius to this day.
My second favourite (if only JRPG-wise): Final Fantasy IX. Yup, lots of folks recommending that one.
Although each new Final Fantasy game takes place in an individual world unrelated to any previous game in the series (excluding "inbetweeners" such as Final Fantasy X-2), the series did develop a tendency to steadily raise the technological level of each new game world - VI had steam engines, VII had cars and computers, and VIII was pretty much the real world, except with magic and monsters.
IX was a one-off throwback to the beginning of the series, with airships being the most advanced tecnology available and civilization mostly limited to one continent, with just a few tiny, isolated settlements scattered across the rest of the world. Here, we see the green forests, stone castles and mysterious, unexplored lands of the NES era, rendered with cutting-edge PS1 graphics! The game is loaded with in-jokes and references to earlier games, but this never gets in the way of the current story, so even if this is the first FF game you play, you won't feel like you're missing out on anything much. Also, it has a great, fast-paced and immersive story.
Incidentally, both games came out on the PS1 back in the day, and are now readily available on PSN!