Here are some things you should inspect in your car on a daily basis:
Fluid levels (engine oil, engine coolant, brake fluid, power steering fluid, and windshield washer fluid)
Fuel level
Tires (tire pressure, signs of wear and tear, etc.)
Lights (headlights, taillights, brake lights, and turn signals)
Wipers
Seatbelts
Jack and wheel brace
Fire extinguisher and first aid kit