Ancestry's free search confirms that there are a fair number of records for different men called "James J Hill".
I cannot access most of the Australian records, but can see this which may answer Mike's question;

"New South Wales Australia, Unassisted Immigrant passenger lists, 1826-1922"

"Name: James J Hill
Estimated birth year: 1879
Age: 17
Port of Departure: New York
Port of Arrival: Sydney NSW,
Voyage Arrival Date: 30 July 1896
Vessel name: Celeste Burrill
Origin location: Geoster"

Searching "Celeste Burrill" gave this excellent list of all onboard for that voyage, including a "James J Hill" from Gloster. This shows all aboard including James are crew rather than "passenger" as the database title implies.
"O.S." = Ordinary Seaman, he's the most junior member of the crew.
http://marinersandships.com.au/1896/07/128cel.htm

Beautiful photos of the Celeste Burrill (built Clare, Nova Scotia) and crew here
http://yarmouthhistory.ca/yarmouthhistory/Albums/Pages/Sailing_Ships_as_Family_Homes.html

Old newspapers carry a few mentions of this British barque, not least an encounter with Malay pirates in 1894; one article from the Melbourne Argos of 27 October 1897 gives an indication to the routine perils of long distance travel in those times;

"The Celeste Burrill as her name implies, a sister ship to the Jane Burrill, and, like the later, she brings general cargo from New York. The Celeste Burrill arrived in Hobson's Bay yesterday morning after a voyage of 93 days. Leaving New York on the 24th July, she on the second day out fell in with a severe W.N.W. gale, but the disturbance proved the forerunner of a long period of fine weather, and the equator was crossed on the 27th August. The S.E. trades were moderate and lasted down to lat. 27deg. The meridian of the Cipe was passed on the 22nd September and shaping a course to run east between the parallels of 39deg. and 40deg., the vessel soon fell in with some particularly heavy weather the wind, however, being from the right quarter. At times it blew with hurricane strength, and occasioned very high seas which broke on board repeatedly but fortunately without any serious results. The meridian of the Leeuwin was crossed on the 18th inst., and westerly breezes brought the ship to port. She is consigned to Couche,Calder, and Co."
http://trove.nla.gov.au/newspaper/article/9776717/308416

The next major port along the coast from Melbourne is Sydney.

Another article from September 1900 describes a longer & far worse voyage also under Captain Trefry from New York to Sydney, when she runs into a cyclone and loses masts and a sailor overboard !
http://trove.nla.gov.au/newspaper/article/14336615

Finally, from Facebook;
"I have been researching and attempting to write about my great grandfather, a lifelong Bluenose seamen from Yarmouth, born in 1860, earned a Mate Certificate in '85, and Masters Cert. in '86. He mastered square rigger ships, the largest being 1,763 tons, from '86-1902 and mostly in the New York-Australia-Manila-New York runs. I own a handful of mementos and a ships painting from his lifetime. After the "Celeste Burrill" was put on her beam ends by a typhoon in the South China Sea, Clarence Trefry ordered that a third of ship's spars and rigging be cut away. She limped into Hong Kong and sold as a hulk to a Manila firm. Dana, Conrad, Melville, and Lundy."
https://www.facebook.com/permalink.php?story_fbid=10150327422901662&id=22451776661

I believe this Yarmouth is the port in Yarmouth County on the southern coast of Nova Scotia. Re Wazza's mention of Nova Scotia, it's highly likely that after crossing the Atlantic most ships would have stopped off there as it's the first landfall since Ireland, with New York their usual destination.

So an interesting ship's history, but sadly at this moment still not certain it carried our James Joseph Hill.

Looking again at the possibles;
GlosBMD gives;

Birth Details
Child Surname Child Forename Father Surname Mother Surname Mother's Former Name Year District Office Register Entry
HILL James Joseph HILL HILL THURSTON 1878 Gloucester Gloucester, Redmarley 14 225

As we know this is our target, he's registered at Newent in both Glos and Herefordshire wrt FreeBMD.

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Birth Details
Child Surname Child Forename Father Surname Mother Surname Mother's Former Name Year District Office Register Entry
HILL James John HILL HILL EAGLES 1876 Gloucester Gloucester, South Hamlet 34 424

Marriage Details
Groom Surname Groom Forename Bride Surname Bride Forename District Parish Building Year Register Entry
HILL James John BROWN Florence Gloucester Gloucester Register Office 1899 16 96

1891, Hopewell Street, South Hamlet, Gloster
Household Role Gender Age Birthplace
Charles Jas Brown Head M 59 Blacksmith. Gloucester, Gloucestershire
Florence Hill Daughter F 22 Gloucester, Gloucestershire
Frederick Brown Son M 16 Gloucester, Gloucestershire
James John Hill Son-In-Law M 24 Bricklayer. Gloucester, Gloucestershire
Charles Jas Hill Grand Son M 1 Gloucester, Gloucestershire

So unlikely that this is the James J Hill sailing alone to Australia.

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However we also find,

Births Sep 1878 (>99%)
HILL James John Martley 6c 287

But Martley is northwest of Worcester, so a fair way from Glos, so seems unlikely to be ours ?.

Surname First name(s) Age District Vol Page
Marriages Dec 1903 (>99%)
Banks Lottie Louisa Worcester 6c 512
HEWLETT Edward Frederick Worcester 6c 512
HILL James John Worcester 6c 512
Price Augusta Elizabeth M Worcester 6c 512

Judging from Family search it seems that this man lived in Broome (Worcs) in 1911, and in Stourbridge in 1915 when he joined the Royal Army Service Corps.
Think we can discount this man.

--------------

HOWEVER, I've just found this, who is he ??
1891, Melbourne Street, Barton St Mary, Gloucester, Glos
John Hill Head M 33 General Labourer. Gloucestershire, England
Eliza A Hill Wife F 31 England
James J Hill Son M 14 Labourer, born 1877. England
Joseph Hill Son M 13 England
Henry J Hill Son M 11 England
Annie L Hill Daughter F 8 England
Edith F Hill Daughter F 6 England

?? HELP !!

thanks for that Mike , i hadn't seen that one clipping before looks like he was a sailor for a few years and that makes it harder to track ,as lots of crews were never registered.well done.