Still in Castelia City...
After beating Burgh, make your way north towards the other end of the city. Colress will interrupt you and challenge you to a battle, however, it is a battle on Route 4, and not at Castelia. He says that he looks forward to seeing your Pokémon in action and leaves it at that. Continuing this way, three buildings can be entered. Enter the one on the left and talk to the old man and he gives you an Amulet Coin, a held item that doubles amount won from battles if the holder participates in battle.
Entering the first building on the right and go upstairs after bring frisked by an agent. On floor 47, talk to the girl in the glasses on the left and you get TM 45: Attract. Attract is a move that infatuates the opponent if it is the opposite gender.
Entering the next building over and talking to a scientist will nab you an Eviolite if you have seen 40 Pokémon in your Pokédex. The Eviolite is an item that boosts Defense and Special Defense by 50% if the wielder can evolve again (for example, Chansey can evolve into Blissey, so if you give Chansey an Eviolite, it gets the boost.) Going up the elevator, and on floor 47, you can get a Charcoal, which boosts the power of Fire type moves.
Right when you leave Castelia, Bianca interrupts you and gives you the Dowsing Machine, or the Item Finder. Really useful for the desert coming ahead.
Moving forward, a Breeder is ready to battle, but Breeders have a gimmick. Pokémon Breeders will always battle you, no matter if you have previously defeated them or not. Good for Experience and money, bad for pace of gameplay. The Hiker informs you that darker sand contains Pokémon. Going left can get you into some of the aforementioned sand and towards a Policeman and further still are two fisherman and a Mystic Water, a held item that raises the power of Water type moves. Going forward, however, is Colress and a line of Crustle. Colress demonstrates his new machine that moves the Crustle, then talks about his opinions of a Pokémon's power being drawn out, and then he commences battle.
Colress has a Magnemite and a Klink. Neither of them is too much trouble, but Magnemite does have Sturdy, which pretty much gives it a Focus Sash.
After beating him, he leaves and you are free to explore more. There are differences between Black 2 and White 2 with this route, as Black 2 has more construction done and it is more modern, but White 2 has ancient Ruins. Items vary between versions, but there is a trade of Cottonee for Petilil (Black 2) and vice-versa (White 2), and they hold Power Items (Anklet and Weight, respectively).
Also on this route is a Mandibuzz (Black 2) and Braviary (White 2). These appear on the route on Thursday (Mandibuzz) and Monday (Braviary) at level 25, and their Hidden Ability. Every week they spawn, and you can save and fight them to make sure you catch them.
TM 28: Dig can be found on this route either nearby a Rich Boy in White 2, or a Policeman in Black 2. Dig is an 80 power, 100% accurate physical Ground type move that takes 2 turns to execute. Turn one is used to dig a hole in the ground, making you immune to moves (except Earthquake, Magnitude, and any move used by a Pokémon with No Guard), and turn two is used to deal damage.
New Pokémon on this route have quite a bit of potential. First we have Darumaka, a Fire type Pokemon that does not seem like much now, but when it evolves into Darmanitan, it gains a 95 Speed stat and a monstrous 140 Attack Stat, backed by Sheer Force, which is pretty much the end of all Grass types.
Next is Trubbish, which he and his evolution Garbodor both get hate for their designs, but they have some bulk and decent movepools to back them up. Poison typing gives them only 2 weaknesses. If you ignored Koffing and Grimer before, Trubbish may be what you are looking for.
Then we have Sandile, which is a really good Pokémon when it evolves. It can either get Intimidate or Moxie, both of which are excellent abilities. Krookodile can fill multiple roles depending on what ability it has. It is a worthy member of any team.
Going straight up leads to Nimbasa City, but going left at the fork leads you to Desert Resort and Relic Castle.