Driftveil City is one of the more memorable places in this game due to the amount of times you will be coming back to this place if you want moves taught to your Pokémon.
When you enter this city, you see two Team Plasma Grunts, one from the old Team Plasma, and one from the new Team Plasma. The new Team Plasma member tries to convince the older one to join their cause, but differing ideals means the older member must decline. Vincent appears and starts yelling at the new Team Plasma member, causing him to run, with your rival giving chase. The older Team Plasma member invites you to come to Older Team Plasma's new meeting place in the city, and then leaves to go to said meeting place.
There is a Calcium laying by the stone bridge you cross when you come into the city. Going to the Pokémon Center and upstairs is a woman who will give you three Luxury Balls. Going to the available house west of it and on the 25th floor is someone who will give you a Big Root, which is an item that increases HP healed from draining moves such as Dream Eater, Drain Punch, and Giga Drain.
Going east from the Pokémon center is another building you can enter. On the first floor, a Move Tutor is here. This one takes Red Shards and tutors moves like Iron Head, Bug Bite, the Elemental Punches, and other moves. Going to the 25th floor, a Gentleman will give you an Air Balloon, and item that acts like the Ability Levitate until the wielder is damaged by an opponent's move. Going further east from the center leads you to a market, where you can buy things like Incense, powders, and other items. There is a secret entrance to this market on the left side, by where Charles is biking. Going through this entrance leads you to TM 63: Embargo, a Dark type status move that makes it so that the target can not have items used on it, or use the item it is holding.
Back outside, Charles will challenge you to the battle you did not fight on Route 5, so in Black 2, you will do a Triple Battle and White 2 will be a Rotation Battle.
Going east from the market will lead you to another accessible building. If you have seen 70 or more Pokémon in the Pokédex, an older man will give you a Shell Bell, a held item that heals damage when the wielder attacks. On the 19th floor of the same building is an Axew that is holding a Haban Berry, a berry that weakens the damage done by a super effective Dragon type move by 50%. There is only one of these, so do not use it, because it will be consumed forever.
South of the market is a building where, on the 25th floor, a butler will give you the Everstone, an item that prevents Pokémon from evolving, but also makes it so the holder will have its nature passed down when it is bred.
Going north from the Pokémon Center is the building that the Older Team Plasma are in. The Old Team Plasma member from before tells Rood that you were the one he was telling him about, and Rood begins to make conversation and battles you to confirm what the Team Plasma member told him. Rood has a Herdier and a Swoobat, both level 27. When he is defeated, he says he now knows you are strong. Your rival comes in and begins to confront these Team Plasma members on where his sister's Purrloin is, for they were the ones who stole it from her five years ago. Rood tells him that he honestly has no idea, and that this part of Team Plasma has given up stealing and has gone into sheltering abandoned and forgotten Pokémon, in which your rival has a meltdown and leaves.
Rood then asks you a favor: take care of N's old Zorua. Rood feels as if you are worthy of it, and will hold onto it if you decline the offer. N's Zorua has 30 IV's in all of its stats, and a Hasty nature, which is almost perfect for competitive usage, if you so which to take it up. It also has N's Trainer ID number (00002), to be able to tell it was his.
Zorua is an interesting Pokémon. Its ability is Illusion, which makes it take an illusion of the Pokémon in the last slot of your party, which makes it a nuisance for Team Preview and when you are against other people. It does not copy the movesets or typing, only the image. When Zorua takes damage, then it reverts back to a Zorua. If it is switched out and switched back in, the illusion is returned. In terms of stats, Zorua is a mixed attacker, but Sp. Attack is a little bit higher than physical. Its evolution, Zoroark is very fast and strong, but fairly frail. Think of it as a slightly slower, but more powerful Liepard (in fact, Liepard beats it by 1 point). Zorua and Zoroark get a signature move, Night Daze, an 85 Power, 95% accuracy special Dark type move, that has a 40% chance to lower accuracy. It is a stronger, but slightly less accurate Dark Pulse, but it works really well on Zoroark. If you did not like what Liepard offers, but admired the type, you cannot do much better than Zorua.
Going back you can see a cave, but it is inaccessible at this point in the game, but there is a Rare Bone down there that cannot be obtained. So the Dowsing Machine is going to throw a fit until it is finally obtained.
Going north and east from the Pokémon Center is the Gym, run by Clay, a Ground type user. Your rival makes on comment on how you should beat it (like we have a choice.) Dewott and Servine will sweep through this, right?