After you defeat Ghetsis in Giant Chasm, Hugh says you should go to Victory Road and challenge the Pokémon League. The west exit of the cave south of Giant Chasm will take you there.
Explore the Route
To fully explore Route 23, you might want to go get Pokémon that know Cut, Strength, and Surf.
When you first enter the route, go north to the small house. The Ace Trainer girl will heal up your pokémon.
If you have Cut or Surf, go south from the Ace Trainer's house to find a Heart Scale past a tree that can be cut with Cut. You can Surf down the river to reach it if you don't have a pokémon that knows Cut.
Now go north and cross the bridge. You'll encounter Battle Girl Brenda, who has a level 53 Throh.
Go north from the Battle Girl to find Ace Trainer Grant, who has a level 53 Emolga and a level 53 Jellicent.
North of the Ace Trainer, you find Hiker Don, who has a level 51 Piloswine and a level 51 Probopass.
To the east of the Hiker, there are some stairs, but if you go past the stairs, you can Surf across the water to reach the house there. Inside, the old man will give you TM35 Flamethrower.
Go back outside, Surf back across and go up the stairs. At the top, you find Ace Trainer Juliet, who has a level 53 Swanna and level 53 Galvantula.
Turn on your Dowsing Machine and go east from the Ace Trainer to find a Rare Candy hidden in the flowers.
Go west past the Ace Trainer, then south. There's a bridge just to the left of the stairs that you can go across. It doesn't lead to the end of the route, but there are trainers and items there, as well as a Hidden Grotto.
If you go south on the bridge near the Ace Trainer, watch out for the fake item in the grass. It's actually a level 56 Amoonguss.
Go east from there to battle Black Belt Luke, who has a level 53 Sawk. Turn on your Dowsing Machine and go south to find a hidden Star Piece on a rock.
Continue south to find an Iron on the cliff just above the house.
Go north, then west on the bridge. The path goes south through some grass. If you have Cut, you can cut the tree for a shortcut to the item (it's a Star Piece). Otherwise you'll have to go south through the grass to get the Star Piece. Note that there is a Hidden Grotto in the trees at the south end of the cliff where you can find the Star Piece.
Now go back to the Black Belt you defeated earlier and go west. Go south down the bridge, then go west. There is a bump in the grass that is actually a PKMN Ranger in disguise. He is PKMN Ranger Steve, and he has a level 52 Stunfisk and a level 52 Amoonguss. After you beat him, he gives you a Sitrus Berry. West of him, you find TM05 Roar.
West from the Bridge
Now that you have explored the area south of the bridge near the Ace Trainer, it's time to go back to the north, then west from the Ace Trainer.
Keep going west to find PKMN Ranger Lena. She has a level 53 Floatzel and a level 53 Lucario. When you defeat her, she gives you a Sitrus Berry.
You can explore Route 23 more if you have Cut and go west from the PKMN Ranger at the base of the stairs. If not, you can just go up the stairs to reach Victory Road. There's a pokémon center there, and you can Fly there, so you could just pick up a pokémon that knows Cut and come back to Route 23 for more exploration. Just be aware that you'll have to watch some cut scenes in Victory Road before you can go to the Pokémon Center there and come back here.
If you go west from the stairs to Victory Road, cut the small tree in the way. Go farther west and cut the tree to the north. If you go southwest, you see some stairs. The item up there is a Full Restore. Down below, push the boulder with Strength.