It's definitely recommended that you bring a car because it makes it much easier to get around St. Louis. Parking on campus is getting better for students, but it could still be improved by adding more spaces. At Maryville, nearly everyone has a car, which sometimes can make it little hard to find a spot, but if you're patient, you will be fine.
The mornings are usually the hardest times to find parking spaces because everyone is on campus. Most days you can luck into a great spot—it will happen a few times—and there will be some days when you just can't find anything. A good rule of thumb is to arrive on campus at least 30 minutes before your class to allow you time to find a spot. You'll often see people driving around the parking lot a few times just to see if someone moved.