After you help Cheryl get through Eterna Forest, you go through the rest of Route 205 and reach Eterna City.
If you use the Old Rod in the water in Eterna City, you can catch Magikarp.
Get an Explorer Kit From Underground Man
Go into the building to the right of the Pokémon Center and talk to the old man. He is Underground Man, and he will give you an Explorer Kit. He demonstrates how to use it to enter the Grand Underground.
There is a Name Rater in Eterna Condominiums, which is the building east of the Poké Mart.
Also in the Name Rater building, you can talk to a kid named Norton, to trade a Buizel and get their level 15 Chatot, named Charap, who is holding a Leppa Berry.
In Eterna Condominiums 2F, the person in the southeast corner will give you some TM67s, which teach Recycle.
If you go northeast in Eterna City, you will meet Cynthia, who will give you some TM93s, which teach Cut. Just by getting these TMs, Cut is added to your Pokétch, but before you can use Cut outside of battle, you will need to get the Eterna Gym Badge. Once you get the Gym Badge, you can check on the small trees that block your path in certain places, and the pokémon will use Cut to cut them down.
East of the Team Galactic building, there is an Herb Shop where you can buy herbs that heal your pokémon, but if you use one, it will lower your pokémon's friendliness toward you.
Route 211 and Mt. Coronet
If you wish, you can go east to Route 211, where you can catch Chingling, Bidoof, Geodude, Hoothoot (only at night), Meditite, Ponyta, and Zubat (only at night). There is a hidden pokéball in the grass there.
Ninja Boy Zach is hiding in an empty patch in the northeast part of the grass. He has a level 13 Zubat, a level 14 Zubat, and a level 15 Zubat. You get 420 Pokédollars for winning.
If you go east across the bridge, you can battle Hiker Louis, who has a level 15 Geodude and a level 15 Onix. You get 780 Pokédollars for winning.
If you use Rock Smash on the rock north of the Hiker, you can go west down the stairs and battle Bird Keeper Alexandra, who has a level 19 Hoothoot. You get 912 Pokédollars for winning.
Go south from the Bird Keeper to find TM12 Taunt.
If you go east to Mt. Coronet, you can catch Chingling, Cleffa, Geodude, Machop, Meditite, and Zubat.
You can't do anything more in this area, so go back to Eterna City for now.
Dawn or Lucas's Father
If you go south from Eterna City, you will find Dawn or Lucas's father. Talk to him and he may give you a Rare Candy if you have seen a lot of pokémon and recorded them in your Pokédex.
When you are ready to proceed, enter the Eterna City Gym.