Terra Haute typically has a supply that exceeds the demand when it comes to rental suites. This doesn't meant that it will always be smooth sailing, but it does mean that there is no real bad time to start an apartment search. As long as you take about two months to look for a place, you should be able to find the right fit.
Affordable apartments in Terre Haute mean that your references and your character are going to be more important than credit or income verification. Make sure you've got good references. Ideally, at least one should be a past landlord and one should be a work reference. If you don't have those, a teacher or a professor can make a good reference as well.
The locals of Terre Haute seem to agree that while the bus system is constantly improving, the best way to get around is still by car. Currently, there is no bus on Sundays and the routes shut down by 6 PM. If planned expansions to serve entertainment oriented areas and the Universities with later hours go through, the bus may become the dominant mode of transportation.
If you enjoy the standard mall shopping experience, then the Honey Creek Mall should be right up your alley. If you prefer local cuisines to chain restaurants, try the Taj Mahal for some authentic Indian food, or Sushi Umi for fantastic sushi. For good music on the weekends, head to the Fourth Quarter, and for the best beer selection in town you can't beat M. Moggers.