Parking at the University is hard to come by most days. Unless you pay the $200 per semester for a residential permit, you will be gambling with finding a spot in the surrounding neighborhoods or on the side of the road down by Lower Campus. If you wish, you can constantly pay money to park your car in a meter spot, but that gets expensive fast.
The police do enforce parking. Many people will get tickets for expired meters or for parking where they are not supposed to park. If you want to be guaranteed a spot, it would be better to just pay the money and get a permit if your finances allow. You do not need a car to get around because the bus system works well, but it is a nice option to have.