I've no reference but believe the use of 上 was linked to "天".
It can be traced to the sentences "上京趕考", "上京面聖", "述職上京". In those, 上京 means 上去京城, for which 京城 was the capital city, where the Emporer (天子) lived and was the respectively the highest location in the entire country (as the sky, 天), thus "going up to the capital -上去京城" was used respectfully.
Also, the ancient Chinese believed a person's soul would going up to 天 after death, 昇天 was used to indicate a person's death, and "昇" was literally meant "上".
At the time capital punishment was still in practice, the executioner would yell at the death roll inmate before execution "xxx, 是時候該上路了 - xxx, its time to going up to the death journey now". Also, the Chinese often associate death with "走" (a person facing death would ask others to do some favors after death and say 我走候... which means "after my death...), so depends on the situation, 是時候該上路了 can be used when one reminds a traveler "it's about time to go on the journey".
Reminder: 上哪去? The question can be abbreviated as both 上哪? and 去哪? But note that 上去哪? is incorrect. Have fun :)