You will be stopped by Alder and he will take you to another Team Plasma speech. Ghetsis talks about the same stuff as usual before leaving. Alder takes you to Drayden and Iris after the crowd leaves and he informs the two of N's plan to have the two Dragon-type legendaries battle. He then leaves for the Pokemon League. Drayden agrees to tell you the story of Zekrom and Reshiram in his house. Follow Iris to Drayden's house. They unravel the story behind the two Dragon-type legendaries. Afterwards, one of them (Drayden in Black, Iris in White) will go to the Gym and wait for you.
Walk upstairs in Drayden's house and talk to the Linebacker to receive the Float Stone. When held, it halves the Pokemon's weight. This can decrease damage taken from moves like Grass Knot. The girl at the other side of the table will give you the Ring Target. It nullifies any immunities that a Pokemon has. For example, if a Gengar holds Ring Target, it can be hit with Normal-type attacks. It may seem like a useless item, but using the move Trick can switch held items between two Pokemon which would give your opponent Ring Target and give you an advantage.
Walk outside and heal up at the Pokemon Center to the southeast. The house on the western-most street has an old man on the first floor that will give you a different prop every day. The house directly north of the Pokemon Center has a girl on the first floor that will tell you if your Pokemon have full EV points. Upstairs in this building is a guy who gives a Cell Battery if you show him a Pokemon that knows Charge that was traded from the game opposite of yours. The Cell Battery is a one-time use item that increases Attack if hit by an Electric attack.
The building to the north is the Rotation Battle House. The guy inside standing by the door will explain Rotation Battles if you forgot how they work. The trainers in this house will battle you once a day. The trainers have switched out their Pokemon in Pokemon White, so the male Ace Trainer has the three elemental monkeys. The female Ace Trainer in pigtails will battle you on the first floor.
Enter the building west of the Rotation Battle House and talk to the girl on the first floor. She will give you the Destiny Knot. When a Pokemon holding it is affected by Attract, it makes the opposing Pokemon fall in love too. The building to the west is the Pokemon Gym of Opelucid City. Enter it once you're ready to take on Drayden/Iris.
Items in Opelucid City:
Received from the Linebacker on the second floor of Drayden's house.
Received from the girl on the second floor of Drayden's house.
Received from a guy on the second floor of the house directly north of the Pokemon Center if you show him a Pokemon from the opposite game that knows Charge.
Received from the girl on the first floor of the house west of the Rotation Battle House.