What transportation options do I have to get from the amtrak station to a hotel in Harvey. Anything that would be less expensive than a taxi?

Jefferson parish tranist(bus) take streetcar from amtrak to library and change from streetcar to bus and it will bring you across the river to oakwood and then you change bus for Harvey from there very easy to do

Nothing that I know of other than Uber.

Uber

http://www.jeffersontransit.org/default.php