Continuing South past the grass and over a bridge will bring you to an encounter with another Battle Girl.

Battle: Battle Girl Glinda (1360 Poke)
Opponent: Gurdurr Lv 40

Keep going South and you’ll run across an Ace Trainer.

Triple Battle: Ace Trainer Junko (2340 Poke)
Opponent: Gligar Lv 39, Lilligant Lv 39, Basculin Lv 39

Continue and then head up the stairs to the West and you’ll find a large grassy area and more stairs.  Scope out the grass and you can pick up a Max Potion near the cliff, as well as getting a chance to have yet another battle.

Battle: Fisherman Sid (1216 Poke)
Opponent: Staryu Lv 38, Buizel Lv 38

Keep going up the shorter flight of stairs and face off with an Ace Trainer at the top.

Rotation Battle: Ace Trainer Kipp (2340 Poke)
Opponent: Tangela Lv 39, Zebstrika Lv 39, Skarmory Lv 39

Keep going West and climb another set of stairs, then head South through the city gate if you like, but the way is blocked by a random group of dancers.  Since there’s no continuing that direction, make your way back to Undella Town.