I need a place besides besides the sewers and Relic Passage to train my Pokemon to about Level 27 to face Burgh. Any places?
One place that helps rack up Exp is the Battle Company next to the Statistics HQ. Other than that, the places mentioned above are the only ones. Burgh's highest LV Poke is LV 24, so you don't need to train to LV 27.
The Battle Company, it's the building two away from the Pokémon center or Pokémon Breeder Irene she is on route 4 before the "rocks", you can battle her infinitely.