Where is the Battle Resort?
It's an island by Ever Grande City.
How do I get there?
In order to get to the Battle Resort you must meet several criteria.
Source: Experience and Bulbapedia
It's on an island between Ever Grande city and Pacificlog town, but only after you defeated the elite four + champion, after you defeated them, you can (indeed sum wun) take the boat at Slateport or Lilycove