Beyond the Pokemon Center is the Battle Institute.  Opening the door gets you intercepted by an Ace Trainer, who tells you that only the strongest can enter- so you can’t return until you defeat the Champion.

In the building to the North of the Pokemon Center you can learn a few things about shiny pokemon.  Upstairs, a woman will estimate the happiness rating of your lead pokemon, and a blue-haired man will hand you a Sun Stone (useful for evolving certain pokemon).  The next building over has a similar state- you can learn about the Wonder Launcher for battles with other players, the Small Court and Big Stadium that are in the North end of Nimbasa, and a woman on the upper floor will give you a Soothe Bell if your lead pokemon likes you a lot.  A Soothe Bell is a hold item that increases the rate at which a pokemon gains happiness, so it’s useful for many evolutions and for the use of the attack Return.

North across the water is the arena area of Nimbasa- Small Court is on the left, and used by tennis and basketball players.  Who is there changes each day, and many of the people on the court will be trainers eager for battle- each day the place is restocked as you enter with trainers using pokemon around the level of yours, so there is no set data for the trainers.  Similarly, Large Stadium holds football and American football practices, with the people (and pokemon) replaced each day.  During the morning, Small Court holds tennis players and Large Stadium has football; these change to basketball and American football in the afternoon.  If you go into the Court or Stadium and defeat all the trainers on the field, you can sometimes get extra items.

To the right of Large Stadium is the Musical Theater, which is exactly how it was in the first Black and White games.

Heading further East from the Musical Theater is a gate, where a baseball player will give you a Macho Brace, and beyond that is a small chunk of route that you can explore already.