The Crystal Ring is a simple, smooth, cyan bracelet that Sonic wears on his right wrist. It allows Sonic to take half the time to charge the Light Speed Dash and the Light Speed Attack.
Using the Crystal Ring also changes Sonic's aura when charging up his techniques from blue to turquoise.
The Crystal Ring is found behind a door inside the hotel in Station Square and can only be accessed via the Light Speed Dash, which can only be done by obtaining the Light Speed Shoes.
First, Sonic has to climb the stairs on the left side of the hotel entrance. On top of it there are two buttons; one to open a door on the other side of the lobby, but only briefly, and the other creates a trail of rings leading to it. Use the Light Speed Dash immediately on the trail of ring to pass through the door in time and the Crystal Ring can be found behind it.
It is also possible to get the Crystal Ring without Light Speed Shoes by using a Spin Dash Jump, but Sonic cannot use the ring before he has the shoes.
Since Sonic Adventure is the only game where the Light Speed Dash requires charging by Spin Dash (having been switched to a single button-press onwards), this may explain why this one-time Level Up Item has not appeared since.
It should be noted that the Crystal ring is similar in appearance and color to the rings that are in Tikal's wrists.
The Crystal Ring can trigger a bug in the original Sonic Adventure if it is collected during Super Sonic's story (as prior to becoming Super Sonic, Sonic roams the Adventure Fields in his regular form and can do everything he is able to do during his own story). If one collects the Crystal Ring then exits the game (as the Crystal Ring would be seen as a story event and prompt an autosave but not have a trigger in-game correlating to the event itself), upon restarting a story brief will play followed by crashing the game in some way.
Sonic obtaining the Crystal Ring
Sonic wearing the Crystal Ring
The Cystal Ring in use (notice the change in Sonic's aura's color)