Those who live off campus, for the most part, live directly off campus—no more than a block away from the dorms. You don't save much money by renting an off-campus apartment, and you miss out on important things like an Ethernet connection, cable TV, and convenience and safety benefits. Because students choose to live so closely, they don't lose out on much of the community feel of Trinity, nor do they receive a greater feeling of independence or individuality.
The only real reason to live off-campus is if you live in a sorority or fraternity house. Those are located on Allen Place, a block from Vernon Place, a main street of Trinity's campus. Each year, several people will also rent houses or apartments on Crescent Street, which is the same street that houses the notorious Sophomore Slums.