The Olympia from 1872 can be found at the following website:
http://www.theshipslist.com/ships/lines/anchor.shtml there was 2 steamships by the name of Olympia Olympia -1 1872 - 1898 Scraped Olympia 2 1902 - 1926 Scraped , before 1855 almost all ships appear to be sailing ships.
Also an A-Z index at the following website:
http://www.theshipslist.com/ships/descriptions/ using this index the only Olympia is from 1872
Your ship Olympia arrived at the Port of New York Oct-1, 1834 with about 70 passengers. This was the only trip to N.Y. made in 1834.
Tim