The Item Ball holds a Carbos, the ‘vitamin’ item for Speed.  After snagging it, return to where the Ace Traner paces- this is now the most important junction in the cave.  If you head North, you can go down to the bottom of the cave.  West is a quick route back to where you entered to begin with.  East is the way out to Mistralton city, and that’s where you should head now.

You’ll see the Pokemon Center immediately, so go ahead and use that as needed.

In the house to the East of the Pokemon Center is a woman who wants to see your TMs.  The more you have, the better the item she gives you when you show her, so make sure to come back every now and again and talk to her.  There’s also an Iron in her garbage for whatever reason.
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As you go to head North from the pokemon center, Professor Juniper appears, walking over to greet you and introduce herself in person.  She has a look at your Pokedex for you, and tells you how you’re doing- then hands you a Master Ball.  This extremely rare item occurs once or maybe twice in any cartridge of any pokemon game- with good reason.  The Master Ball never fails to catch what it is thrown at- as long as that pokemon can be caught, it will be.

Juniper explains this, then mentions that she’s surprised at how much the region has changed- in just two years, the distribution of pokemon has drastically altered.  As she muses on how this keeps her in work to do, she’s interrupted by someone calling for her.  As it turns out, the shouter is none other than Skyla, Mistralton City’s Gym Leader.  Juniper greets her and introduces you, though Skyla notes that the professor shouldn’t be surprised: Juniper had asked to get a ride in Skyla’s airplane to Twist Mountain.

Juniper cheerfully agrees, but asks Skyla to wait until the professor is done checking out Celestial Tower.  That said, she turns and heads off to the Northeast.  Slightly put out, Skyla complains about the impossibility of deciphering Juniper- she’s not sure if the professor is too relaxed or just oblivious.