Check the following locations to find the keys:
Alaskan Tundra: Jump over the tower near the airplane hangar to pick up the key for the Snowmobile.
American Gothic: Go near the railroad tracks. The key for the 450 Dirtbike can be found on the roof of the building connected to the railroad.
Bayou Delta: The key for the Trophy Truck is on a little island where the finish is located in Time Attack. Ride as fast as you can into the water. You should get the key even though you will crash.
Seaside Links: The key for the Golf Cart is on the balcony of the Marquee jump. Hit the tent that is shaped into a jump, and grab the key.
Yucatan Ruins: The key for the Buggy is located in the courtyard with the water fountain in the middle. The key is on top of the fountain. To get it, simply get on top of the courtyard, then get on the arch, and ride off onto the key.