I believe Adams made the first mention of the chanty "Tom's Gone to Hilo."

1879        Adams, Captain R.C. _On Board the Rocket._ Boston: D. Lothrop & Co.
PDF and TEXT FILE

It's ca.1865-1869 on the barque "Rocket." Adams is speaking in general about chanties though.

Where Tommy actually proceeded to when he went "a high low" nobody knows, but the fact is related with continual gusto nevertheless: —

TOMMY'S GONE, A HIGH LOW

My Tommy's gone and I'll go too;
    Hurrah, you high low.
For without Tommy I can't do.
    My Tommy's gone a high low.
My Tommy's gone on the Eastern Shore,
    Chorus. 

My Tommy's gone to Baltimore,
    Chorus.

A person who knows a little of geography can send Tommy around the world according to his own discretion.

Notice that the phrase is "A high low," not "TO high low."