Hi I wish you best of luck I know this hunt has to be some what challenging.
I think you might have better luck looking for a home rental.
Here is a list of property managments in the area
Property Management in Lexington, NC on Yahoo! Local.
Far as the apartments
Regent's Center might be more pricey it the newest apartment complex. I am concern about Fairview Village due to age they was probably the cities first apartments and they might have done some updating I would be concern about having problems that detoriate over time like plumbing and wear and tear. They are least 30 years old.
Location very central across the street from Country Club area but also has sketchy neighborhood on its backside.
You might also look up Forst Ridge apartments if you got a job with lexington city schools and with the middle and high school you are in walking distance to the school. It is in ok area.
Lexington is a decent city I know very little about Michigan but Lexington is a very laid back town but very good central location to larger cities
when I lived there I like the options of being able to visit other cities and not being such a hazzle to go to them, nor deal with issues that plaques thouse areas.
Fun cities that are nearby are Winston Salem within 15 to 20 minutes, Greensboro 30 minutes, and charlotte is within a hour.
It is a overall safe city like any town has a few sketchy areas but they are very small areas and your fellow teachers will be glad tell you what few blocks they are. A great area to get involve in the community as well.