The first secret is a drivable version of Kaneda's bike from Akira.

Next to the apartment building you are sent to at the start of the game, there is a highway junction that gives you access to the upper level of the city. When you come to a split in the road, follow the left path and continue until you find yourself in an open area. Kaneda's bike will be on the left side next to a ramp. There are multiple ramps on the map, including one by the docks. You can drive the bike as you would your car, however it will respawn at its original location upon closing the game.

The second secret is a jetpack.

Navigate your way to the Trashfields. The most direct route I've found is via a tunnel behind your apartment building. At the end of the tunnel, you'll come to a junction. Turn left and continue along the path. Eventually, you'll find some terrain blocking the road. Go over this terrain and you'll find a place I've dubbed Trashtown. There will be a woman standing in the middle of Trashtown. Exhaust her dialogue and she will give you a jetpack. The jetpack works by jumping and then holding down the jump key while in mid-air. It has a limited charge which refills over time.