Harrisonburg is very much a college town, so there are many landlords who are prepared to and used to renting to students. Start reaching out in February or March and you can get added to wait lists for when places start opening up in the spring.
James Madison has a great off-campus life (OCL office) that helps students adjust to off-campus life successfully. They offer a listing service for landlords that rent to students, as well as a roommate matching service that is extremely helpful for out-of-towners without existing connections at the University.
Harrisonburg is a driver's city. However, if you live near downtown, you can walk almost anywhere, and there is limited bus service that connects the city to the University. The city has made plans to upgrade its bus fleet and transit routes, so better bus connections may be available in the future. At present though, it is best to either bring a car, or pay careful attention to location when selecting your apartment.
The University campus is one of the most beautiful and scenic places in the city to take a walk. If you want to catch some live music, Clementine's is a local watering hole known for getting worthwhile acts in. Getting out of the city is a great way to spend some free time as well. The fishing, hiking, cycling and camping just outside the city appeals to many of the tourists who come to town, and if you're new to town you should try to make the most of it.