I'm going to a hospital that's far away from my house today.
I'm going to a hospital that's near my house today.
ーI'm going to a hospital that's far away from my house today.
「今日は家から遠くの病院にいきます。」
far away で「遠方の・遠くの」
=that's quite a distance from my house と言うこともできます。
distance で「遠方」
ーI'm going to a hospital that's near my house today.
「今日は家の近くの病院へ行きます。」
=that's close to my house と言うこともできます。
close で「近い」
ご参考まで！
カナダ 
