Sen to Chihiro no Kamikakushi, Hottarake no Shima: Haruka to Mahou no Kagami Recommendations
Both are stories where a young girl is transported into a visually-stunning magical fantasy world and has to overcome various challenges before returning to the real world. Both reference youkai and folklore, where the main character must befriend and interact with them.
It will be actually one-sided recommendation - most people at least heard of Spirited Away. Hottarake no Shima, however is very underrated in my opinion. Just like in Spirited Away, we have a young girl who wents into the world of magic and encounters it's strange inhabitants. Both movies have beautiful visuals, Hottarake no Shima, however, is CG while Spirited Away uses the traditional animation. Even if you're not a fan of CG, give it a try, because good anime movies are becoming a rare thing. Especially family-friendly ones.
Lead protags are both cast into unfamiliar, and bizarre territory. The focus and struggles with family will tug at your heart strings.