The best time to rent an apartment in any college town is April through June. This definitely holds true in Jonesboro. Students who know they are leaving town typically start giving their notices to vacate in April. If you start looking around then, you shouldn't have any problem finding a place soon, as more vacancies will also pop up throughout May and June.
Dealing with Jonesboro landlords is usually a pretty straightforward affair. The big thing to remember is that you need to be honest with landlords. They are going to follow up on everything you say, so you don't ever want to try and fib to them during the application process.
There is a small public transportation system in Jonesboro, but it's limited to weekday routes. Most people in Jonesboro choose to either drive or bike everywhere they go. The city is very bike friendly, and the bus system even has bike racks on the fronts of their vehicles to encourage cyclists to ride the bus for longer hikes across town.
For the most concentrated shopping in town, you probably want to go to the Mall at Turtle Creek. Most of the local bars are all found downtown, in a small entertainment district. There is also a local nature center where you can either go for a hike, or relax in a viewing area.