Rural area/countryside — a non-urban place with more nature; often carries the nuance of being peaceful but less convenient.
田舎は空気がきれいで、夜は星がたくさん見える。
The countryside has clean air, and you can see lots of stars at night.
都会で暮らしていたが、子どもの頃の田舎が恋しくなる時がある。
I lived in the city, but sometimes I miss the countryside of my childhood.
田舎では電車の本数が少なく、移動に時間がかかる。
In rural areas the number of trains is small, so travel takes time.
Hometown — the place where someone was born and raised; can convey affection or nostalgia.
彼の田舎は北海道で、冬は雪が深いそうだ。
His hometown is in Hokkaido; I hear the snow is deep in winter.
田舎に帰ると、家族や昔の友達に会えて落ち着く。
When I return to my hometown, I can meet family and old friends and feel at ease.