Nacrene City is home to a bunch of warehouses that have been converted into homes and stores. You will meet Cheren here, who gives you some Chesto Berries.
Encounter with N at Nacrene Gym
When you try to go into the Gym, N steps out and tells you his vision for the future of pokémon. It sounds a little shady to me. But whether you agree or disagree with what he said, he will challenge you to a battle. He has a Pidove, Timburr, and Tympole.
It's a good idea to bring a grass or electric type pokémon with you into the battle, because Tympole can be kind of tough otherwise. If you didn't choose Snivy as your starter, you can try to catch Blitzle in route 3, or you can look for grass types in Pinwheel Forest. As for Timburr, Munna is probably your best choice, because Timburr knows Rock Throw, which means that even though Pidove has a super-effective move against Timburr, it will be vulnerable to that Rock move. As for N's Pidove, it's weak to Rock, Ice, and Electric, so Blitzle could be a good opponent, or Roggenrola.
After you defeat N, he will declare his intention to capture Reshiram (if you're playing Black) or Zekrom (if you're playing White.) Then he will walk away.
Exploring Nacrene City
In the café, the person there will tell you that they have a special on Wednesdays. If it's Wednesday, she will give you a free Soda Pop. Outside of the café is a guy playing the accordion. You can hear his accordion added to the town music if you're close to him.
In town, you will find someone selling battle items like X Accuracy and Dire Hit. There is someone in town who will ask you to trade a grass type pokémon with her. After you do, she will want to battle.
Exploring Outer Pinwheel Forest
You should head over to Pinwheel Forest to the west. The inner part of the forest is blocked off by a bunch of Team Plasma grunts, so you can't go into the interior of Pinwheel Forest yet. The outer area of the forest has some fighting pokémon in the grass that will help out in the Normal-type gym that you will soon face. These include Timburr, Throh, and Sawk. Also, someone here will give you a TM for Rock Smash. There is also a Nurse who, once you defeat her, will heal up your Pokémon for free whenever you talk to her.
If you go south and then east up some stairs, you will find some Black Belt trainers, as well as a large boulder. This boulder is the Challenge Rock that those two trainers will talk to you about. If you have a Fighting-type pokémon in your party, you can check on the Challenge Rock, and the fighting-type pokémon will punch it, which will chip off a Star Piece from the rock. You can only get one Star Piece per day from the challenge rock. You can sell the Star Piece for 4900.
Prepare for Nacrene Gym
The next Gym leader, Lenora, runs a gym specializing in Normal-type pokémon. Lenora has a level 18 Herdier and a level 20 Watchog. You might want to train your fighting types up to at least level 20 before proceeding on to the Gym.
When you're ready, stock up on potions and go to the Nacrene Gym.