Straight off the boat, go to the edge of the pier to find a Heart Scale. It will come in handy later if you want to have a Pokemon relearn a move it has forgotten. Exit the pier to the north where a Harlequin gives you a bike. This is probably the most useful item in the game. It lets you move much faster than you do while running. Be sure to register the bike in the item menu by highlighting it and pressing Y. This way, you can just press Y to hop on and ride whenever you want. Go to the Pokemon Center to heal and stock up on items.
From the Pokemon Center, walk right until you find the Skyarrow Bridge Gate. Inside is a female Clerk that gives you a Quick Claw. The Bridge is closed off for now, so go back to the Pokemon Center. The areas directly to the right of the Pokemon Center are Cruise Dock and Castelia Street. Cruise Dock has a large cruise liner, but you can't ride it yet. Castelia Street has two buildings. The one on the right is the Game Freak building. On the 22nd floor you can find a Revive and two trainers sitting at a table waiting to battle.
The building on the left side of Castelia Street has a guitarist on the 11th floor that gives TM 44 Rest, which heals a Pokemon's health but also puts them to sleep. That's everything on this street so move left to Mode Street.
There is a museum on the right side of Mode Street. It has a guy in a suit that asks to see a specific thing every day. If you show him, you'll get a prize. The left side of the street has the Casteliacone stand. Casteliacones heal all status ailments. Move to the next street to the left, Narrow Street.
Just like its name implies, this street is very narrow. When you walk past the dumpsters on the left, a man pops out and gives you TM 70 Flash. It can be used in battle to lower your opponent's accuracy or outside of battle to light up dark caves. The entrance on the right side of this street leads to a cafe. Talk to the clerk to receive a Moomoo Milk. This is also the place to change Meloetta's form.
In between Narrow Street and the Pokemon Gym road to the left is the Passerby Analytics HQ. It's where you can set up some questions and answers for the surveys you can take with other people who play Black and White 2, but it isn't very important.
The next road has the Castelia City Gym. Clyde, the white-haired guy, is standing in front of the door. Talk to him and Iris shows up. Before too long, she leaves for the Castelia City Sewers at the right-most dock of the city. That's eventually where you have to go, but for now it doesn't hurt to continue exploring the city.
The building on the opposite side of the gym has a girl on the first floor that massages Pokemon to raise their happiness. There is also an old man that lets you rename your Pokemon. Floor 2 has a man that explains the new Medal system. Floor 3 is the new hangout for Fennel and Amanita. They can explain the C-Gear and Dream World to you. Go north to the city's hub. There are some vending machines here to buy drinks. Continue north to the final street in Castelia City.
The building on the left has an old man that gives the Amulet Coin. It doubles the amount of money you gain from trainer battles if your Active Pokemon wears it. The 11th floor has nothing worthwhile, so go to the first building on the right side of the street. There is an international party happening on the 47th floor. The girl in pig tails gives TM 45 Attract. This move infatuates the opposing Pokemon if it's the opposite gender of the user. An infatuated Pokemon only has a 50% chance of performing a move successfully.
The other building on this side of the street has a scientist on the first floor that gives an Eviolite after you've seen 40 Pokemon. When held, Eviolite raises the Defense and Special Defense of a Pokemon that isn't fully evolved. There is a Charcoal on Floor 47, which increases a Pokemon's Fire-type attacks by 20% when held. There is also a man that explains each gym badge and their effects.
The last thing to do in Castelia City before meeting with Iris in the sewers is to go through the Battle Factory. It has a lot of trainers to battle for experience and an awesome item. The Battle Factory can be found in between Mode Street and Narrow Street.
Items in Castelia City:
After arriving in Castelia City, walk to the south end of the pier.
Given by a Harlequin after leaving Prime Pier.
Received from a female clerk at the Skyarrow Bridge Gate.
On the 22nd floor of the Game Freak building.
TM 44 (Rest)
Received from a Guitarist on the 11th floor of the building on Castelia Street.
Can be purchased on Mode Street.
TM 70 (Flash)
Received from a man that jumps out from behind the dumpster on Narrow Street.
Given by the barista in the cafe on Narrow Street.
Received from a man in the west building on Castelia's northern-most street.
TM 45 (Attract)
Given by a girl in pig tails at the international party.
Received from a Scientist at the northern-most building in the city.