Norfolk is a large enough city that it has a lot of available rental properties. There tends to be relatively stable availability throughout the year, but the options seam to peak in the summer. Try to find your apartment sometime before August to ensure that you have enough options to choose from.
In Norfolk, the affordable prices are going to make other parts of your application at least as important as your proof of income. Spend some time getting good references before you apply for your apartment. Reach out to your references beforehand and ask permission to use them. If they seem surprised when a prospective landlord contacts them, it could hurt your chances of getting approved for an apartment.
Driving in Norfolk can be confusing, and it can take some time to learn how to navigate the city by car. Public transit however, is available, and should be able to get you to most of the important areas of the city. Hampton Roads Transit offers buses, a light rail system and a Trolley Tour around the city.
The sea and the military are very important to Norfolk's history. Visiting the Naval Museum, Nauticus and the Battleship Wisconsin are great ways to get a sense of the grand maritime legacy of the town. Other sea-faring activities such as short cruises and fishing expeditions are very popular. To enjoy the nightlife, you need to head down to Ghent or to Granby Street.