After you defeat Burgh, you get the Insect Badge and can continue your journey. Your next stop will be Nimbasa City, but you have to go through Route 4 to get there. In Black 2, there are a bunch of buildings in Route 4. In White 2, they abandoned the construction here because of finding the ruins.
Go north from Burgh's gym and you will reach Central Plaza. The weird guy that you saw in the sewer, who has a blue thing in his hair, shows up and asks to see your pokémon. Say yes. He says that he is a scientist named Colress. He asks you to battle him. He will be waiting on Route 4 to the north.
When you go north, Pokémon Breeder Irene will challenge you. She has a level 16 Drilbur and a level 16 Marill.
Important! Pokémon Breeders will always challenge you every time they see you. This is not a glitch. If you want to avoid Irene next time, you have to walk as far left as you can past her. She won't see you if you are that far away.
There is sand to the left. You will encounter wild pokémon in the deep sand.
You will encounter Policeman Braven, who has a level 16 Growlithe and a level 16 Herdier.
To the west, there are stairs leading down to some water. There is a Mystic Water to the south.
The fisherman at the top is Fisherman Hubert. He has a level 17 red Basculin.
Fisherman Andrew is to the south of that. He has a level 16 Psyduck and a level 16 blue Basculin.
When you go farther north on route 4, you encounter Colress, who is standing in front of a wall of Crustles. He uses a device that he created to energize pokémon, which makes the Crustles go away. Colress disagrees with Team Plasma's belief of liberating pokémon. Instead, he believes humans should bring out the full potential in pokémon.
Now you must battle Colress. He has a level 21 Magnemite and a level 23 Klink.
After the battle, Colress sees that you bring out your pokémon's power by being kind to them. Colress gives you a Protein. He wishes there were someone who can talk to pokémon. Colress goes away, and now you can explore the rest of route 4.
Go North on Route 4
In the second house on the right, there is a girl named Calla. If you are playing Black 2, she will give you a Petilil in exchange for a Cottonee. If you are playing White 2, she will give you a Cottonee in exchange for a Petilil.
Upstairs from the girl, there is a Wide Lens to the left of the TV.
In the house to the north on the left, there is a martial arts guy upstairs who gives you Sitrus Berries.
To the north of that, to the right, there is a maid on the lower floor who will imitate the sound of a pokémon in your party, then asks you which one she imitated. If you give the correct answer, she gives you a Poké Toy.
There is a shiny building up north, but first, go left to explore the rest of the route.
You encounter Policeman Dell, who has a level 21 Riolu and a level 21 Growlithe.
Nearby, there is a hidden Red Shard that you can use the Dowsing Machine to find.
You will also find Policeman Neagle, who has a level 22 Herdier.
You can find TM28 Dig somewhere near here.
Check for a hidden Hyper Potion in this area.
Soon you find Roughneck Joey, who has a level 21 Venipede and a level 21 Sandile.
Also look for Roughneck Silvester, who has a level 22 Darumaka.
Search for Stardust nearby.
There is Biker Stanley here. He has a level 21 Zubat and a level 21 Timburr.
There is also Youngster Sinclair, who has a level 22 Pidove.
Near him is a Grip Claw. Also search for a Yellow Shard, Stardust, and Green Shard.
Soon you find Hooligans Rob & Sal. They do a double battle and have a level 21 Cottonee and a level 21 Petilil.
There is a house nearby where a woman will heal your pokémon for free.
To the north, you can find Relic Castle.
There is a shiny building in the north part of Route 4. Go inside to find Join Avenue. Agree to manage Join Avenue, then tell him the phrases that he asks for.
Tell the blue-haired girl what you want to be called. She explains about Join Avenue. The way it works is, if you meet people in the Pokémon Dream World or interact with players over Wi-Fi or the Nintendo WFC, they might show up in Join Avenue. They will want to open a store there.
Then when regular customers walk by, you can talk to them and recommend a store. If you recommend a good store that the customer thinks is interesting, the popularity of that store will go up, which increases the popularity of Join Avenue. New features get added as your Join Avenue increases in level.