Hyrule Circuit

Shortcuts

You can use two mushrooms after the beginning to get to the ramp and skip the next turn.
After exiting the castle, you can use a mushroom to drive over the left grass patch.
Alternatively, you can use a mushroom or a mini turbo to drive through the trees. This is faster, but it skips the third item set.

Hyrule Circuit is primarily a running track, but power items are still useful.
Aside from the shortcuts, Golden Mushrooms and Bullet Bills can be used at the second set to speed ahead before the third set/NISC shortcut.
Traps are best positioned at the first S turn, the castle section with the Master Sword, the S turn before the third set, and the final split paths.