Corpus Christi is a large enough city that location matters. This means you want to give yourself at least an extra month to make sure you find one in the part of town you need to live in. Give yourself at least 8 weeks before you needed move-in date.
Check with your school for a list of apartment buildings that are known to be student friendly. The major Universities and the smaller colleges all maintain lists of these types. This can help get you the inside track on good apartments close to school, even if you're not familiar with the city beforehand.
There is a public bus service in Corpus Christi, but the city is designed for people who use their cars to commute. If you aren't bringing a car to town, look for an apartment near your school or job. However, most people find it much easier to navigate when they own a car in this particular town.
For your first outing in Corpus Christi, you absolutely have to check out the Bayfront. This scenic walkway comprises two of the most scenic miles in town and is home to many of the best festivals in town during the summer. Couple that with great beaches and water activities, and out of the world seafood, and you'll see that most of the entertainment in Corpus Christi takes great advantage of the Oceanside location.