Finding an apartment in Rochester is not too hard throughout most of the year. Although you could probably find a place at any time of the year, the summer will be the easiest. Many of the places in the city open up starting in early summer, and looking at this time will give you the most options.
When you're renting in Rochester, you should be able to let the landlord know why you're looking to live in Rochester specifically. It's a small town that the residents feel a lot of pride in. If you're moving to the city to work or play in Rochester, they're going to be very happy to have you.
The size of Rochester means that you can walk almost anywhere without any difficulty. Having a car in Rochester can come in handy if you want to commute to Detroit or any of the other surrounding towns, but if you're staying close to home you can do very well on foot.
Rochester is a very quiet little town. If you're looking to grab a bite to eat or head out for the evening, wandering down to Main Street is your best bet. It's less than an hour from Rochester down into the heart of Detroit however, so if you want big-city shopping or to take in a Lions game, you definitely have that option.