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New Haven is the first real town you'll come to. It has all a new trainer needs: A shop, a guardian center, a training hall and a teleporter. As the first town, it's also where you'll learn how to capture and train guardians. Multiple quests will lead you to train a strong team of at least four guardians, before going for your first badge, the Star Badge.
There's a shop, stocking potions and other items, including capture discs.
Even further to the left, you'll find the inn. It's a little establishment which, for 10 tokens, will let you fight every trainer you already fought (not including the Masters) and every iron chest you have already opened, even if 24 hours haven't passed. Note that trainers won't give TT again if fought this way.
The Guardian Center is at the full west of the town. It's a cute building where you'll find Doctor Hows and his assistant. The latter will be able to upgrade the existing capacity of your guardians or teach them new ones, provides Guardian selling and buying possibilities (and also sells some premium stuff), while Dr. Hows will heal your active guardian team to it's fullest.
Finally, in the center of the town is the Training Hall. Here, you'll have to face various trainers before finally reaching the Master. Defeat him, and you'll win your first badge!
If you want more details, beware! Here's a spoiler. Yeah, behind this question mark. Heavy spoiler, for sure!
I warned you...
He is, in fact, the one who gave you your first guardian, the same one who taught you how to train and take care of your guardians. Here's his team (knowing that two of his elemental guardians will be of the type that's strong against your starter guardian, therefore weak against the guardian you got in the forest from Trainer Jill) :
■ Fengal Level 14
■ Kowa Level 13
■ Orkhan or Flicker or Zaat Level 12
■ Psiwren or Bhadusa or Tukker Level 15