To find an apartment you're going to want to be the first on the ground in order to get a great place. May is a fantastic time to look, as this is when the recent crop of graduates is likely moving our of their prime University apartments.
A news expose from 2011 revealed that many Cape Girardeau landlords were not meeting the requirements laid out by the local law. Do your research before you sign a lease and hand over any money. Some time on the Internet searching out any background on your proposed apartment or landlord could save you from getting into a bad situation.
The Cape Transit Authority offers bus service in Cape Girardeau. The service is somewhat limited, but does provide connections between the busiest hubs in the city. However, if you want great mobility a bicycle is the way to go. The city has spent years and a huge amount of money installing dedicated bike lanes, making it a convenient, affordable and green means of transportation.
If you've already got your bicycle for transportation, you might as well enjoy it for recreation as well. The cycling trails both in and out of the city are amazing. History buffs can live in the city for years and still not have seen all of the historic sites that surround the town. If you're attending school, and wondering where all your classmates are headed after dark, try checking out The Library, a local bar that is a favorite with the student crowd.