There is only a limited amount of rental housing in Notre Dame, and vacancies strictly follow the school year. If you want to shop, April and May are really the only times to look where you will gain any sort of an edge. Shopping at any other time of year will require a more atypical circumstance in order to find vacant apartments.
Landlords are going to expect that you're affiliated with the University when you're moving to Notre Dame. Be prepared to answer some questions, either formally on an application or informally, that relate to what you're doing at school. Landlords might want to know what year you're going into, whether you're on a scholarship, if you're an athlete, or other similar questions.
Public transportation is offered both by the University itself, and by SWEEP. SWEEP operates routes throughout the area, and through the connection to Notre Dame you can get almost anywhere you might want to. There are also free shuttles operated by the University for navigating the large grounds. The University also has golf cart and car rental services.
Everything here centers on University life, so the entertainment does as well. Watching the Fighting Irish compete is probably the most popular of all past times with the locals. For those new to town, touring the beautiful campus itself can be very enjoyable. If you're looking for a drink, you should head into nearby South Bend, where there are a variety of popular local pubs.