Here is one web site that can help you learn about Fairbury.
http://jefferson.unl.edu/fairbury.htm
There is a small Wal-Mart on Nebraska Hwy 15 on the north side of the town. You are about forty miles from a Super Wal-Mart in Beatrice. The business district is very good in shopping in the downtown part of Fairbury considering that it is a small town. You will find the majority of the people there friendly and willing to welcome you to Fairbury.
I live in a small town north and east of Beatrice and have been in Fairbury many times. I will try to help you out as best as I can.
They have a bi-weekly newspaper that is covers Fairbury, but it is not currently a on-line newspaper so I can not help you out concerning rentals. You might contact a local realtor to see about this. You might also check out the Beatrice Daily Sun which is on line and see if they have any posting concerning rentals.
Have you ever lived in Nebraska before?