According to The Littlest Hobo on Wikipedia:
All three productions revolved around a stray German Shepherd, the titular Hobo, who wanders from town to town, helping people in need. Although the concept (of a dog saving the day) was perhaps similar to that of Lassie, the Littlest Hobo's destiny was to befriend those who apparently needed help, portrayed by well known actors in celebrity guest appearance roles. Despite the attempts of the many people whom he helped to adopt him, he appeared to prefer to be on his own, and would head off by himself at the end of each episode.
Never actually named on-screen, the dog is often referred to by the name Hobo or by the names given by temporary human companions. Hobo's background is also unexplained on-screen. His origins, motivation and ultimate destination are also never explained.
So, I'm taking it that Wikipedia knows better than you do (it was 3 separate prodcution runs) or me (had never heard of it before today) & the ultimate destinaion, let alone 'home', are never mentioned.
Hobo was a lone gun, keepin' it real (& homeless)..