As previously mentioned, there are three Chao Gardens for your Chao to live in. You must first explore the adventure fields in order to find and access each of the Chao Gardens. Once you have entered a specific Chao Garden for the first time, it will be considered unlocked for that character. Each garden contains two teleporters that individually become active once you've visited at least two different gardens - they allow you to jump and transport Chao and items between gardens without having to run through the rest of the game. This allows you to conveniently teleport between your unlocked Chao Gardens, to better manage your Chao or to simply take shortcuts between the adventure fields.
The Station Square Garden
This is probably the first garden that you will discover. When you first enter it, you will find that it contains two Chao eggs to help you begin your journey with Chao.
This Chao Garden is located within the Station Square adventure field: simply walk into the left lift/elevator in the lobby of Sonic's hotel and you will be taken directly to the garden on the second floor.
This garden is complete with grass, trees, pavement, a pond, and a beautiful fountain. It also contains the entrance to the Chao Stadium
The Mystic Ruins Garden
Run to the left of the stairs leading up to Tails' house in the main area of the Mystic Ruins to find a small cave. Jump into the mine cart at the back of the cave and you'll ride through the gates into the garden on the other side.
This is probably the second garden that you will discover. When you first enter it, you will find that it contains two Chao eggs just like the other gardens.
This garden is like the rest of the adventure field, with lots of grass and a lake and island in the middle of it. There is also a separated stone bridge accross the middle of the garden.
The Egg Carrier Garden
This is probably the last garden that you will discover. Like the others, this garden also contains two Chao eggs.
Head into the main section of the Egg Carrier. You can get there by taking the large golden pod in the middle of the top deck, or via the sky-train located on the lower level to the side. When you get there, run up the stairs to find a door at the top with large yellow pads set on the floor with letters on them. Jump onto the pads to spell out the password EGGMAN to open the door. Head inside then step on the teleporter to be transported to the garden!
This garden has a beautiful beach surrounded by a clear ocean. There is also one of Eggman's large missiles burried into the side of the garden! At the top of the small cliff there, you will find the teleporters and also a sattelite dish rotating round very quickly.