Lot line restrictions? Coop restrictions? ... Washington, IL

That is a tough question.  There is no right answer for all occasion.  My town has 10' off-set for any structure (except fence).  Some towns have defined the size of structure or flock depending the neighborhood.   But how do you define the level of aesthetic?  It is a matter of personal taste.  Same could be said about a dog house. 

The lots in my town vary from 50x100 to acres.  I am on the lucky side.  I have read that some urban areas have 4 or 6 birds limit.

Given all the rules, if the keeper does not maintain the flock properly, nuisance ordinance can be invoked for noise, smell, and yes, unsightliness.

I'm not sure exactly how the older part of Washington is laid out.  Many lots around here are 45' wide so a 20' setback eliminates a lot of people.  I think the way the ordinance proposal has been written we just have a 25' setback from a neighboring residential structure.  With our deep but narrow lots many people can work with this.

I don't think there is a way to legally define "unsightly".  Put Jon to task and ask him how they regulate the construction of dog houses.  I have a neighbor that built their "dog house" out of used pallets with a sheet of OSB over the top. Even I'd consider that unsightly.

My area has 10 ft. setbacks, and anything over 120 sq. ft requires a permit.  There are no restrictions on appearance, and it would be very hard to define appearance without specifying a particular design.  You might want to consider looking at any language that exists for describing sheds or other outbuildings  for inspiration.