Similar to Homesickness:
* Nostalgia: A bittersweet longing for the past, often associated with a specific time or place.
* Saudade: (Portuguese) A deep emotional state of melancholic longing for an absent something or someone that one loves. Often described as a profound melancholic feeling of emptiness, incompleteness, or longing for something or someone that is lost or unattainable.
* Fernweh: (German) A longing for faraway places, a desire to travel and explore.
* Hiraeth: (Welsh) A homesickness for a home that no longer exists, or for a place that you cannot return to.
* Sehnsucht: (German) A deep longing for something undefined, a yearning for something more, a feeling of incompleteness.
More Specific:
* Anhelo: (Spanish) A yearning for something or someone unattainable.
* Heimweh: (German) A longing for one's home, particularly experienced by someone who is away from home.
* Toska: (Russian) A deep spiritual anguish, a feeling of profound melancholy and emptiness.
The best word to use depends on the specific context and nuances of the feeling you want to express.