It would probably take you less time to park in your hometown and walk to Trinity, than it would take you to find a good parking spot at Trinity especially if you aren't one of the lucky few awarded a parking pass each year. Freshmen aren't allowed cars on campus; however, many freshmen still have cars. It's not clear how they do it, but apparently there are ways to get around the restriction. There is major construction on Trinity's campus right now, and the parking has been reduced substantially. Even if you are a senior, you are not guaranteed a parking spot. Only 34 percent of students have a car on campus. The fact that freshman do in fact bring cars, compounded with the constant construction on campus, is probably why there are so few parking spaces.
That said, if you have a way of bringing a car, bring it, despite the parking restrictions. You'll never be able to see the few fun things Hartford has to offer without a car, unless you spend four years bumming rides off friends, as many of the students do. If you end up bumming rides, by the way, be sure to remember to give your friends gas money once in a while.