The best time to look for an apartment in Salem is between January and February. There usually aren't that many people apartment hunting in northern cities at this time of year, so it is a great way to reduce the competition. If you look during these months, you might be the only person looking at a given apartment.
When you apply for an apartment in Salem, be up front with the landlord about why you are moving. If you are coming to town because you've got a new job or because you've been accepted to school, they already know you have a valid reason to come there. If you're moving within Salem, just let them know that you're moving out on your own, or give a good reason for changing your accommodations.
You shouldn't have any problem navigating the small city by foot. If you do need to make a lengthy commute on a regular basis, it is best to have a car. Salem is far enough north that it can get regularly strong winters, so if you're not used to winter driving be sure to take it slow. Winter tires are also strongly recommended.
Salem is home to a number of historic sites that inform visitors about the town's history. There is even a Witch Museum, and a Witch Dungeon Museum. Just taking a walk around town will let you drink in some of the best architecture in the northeast. The city has also capitalized on its past infamy, and is now home to a number of fortune readers and magic-themed shops. The town is a lot of fun around Halloween, with events across town celebrating the haunted season.