How do i know where is a good place to hunt coyotes?

i live in battle creek michigan and i want to go coyote hunting but at our house we have like 15 acres and a river in the back i dont hear coyotes at night howling or anything but theres deer , turkeys and a river and a pond so it would be a good area with lots of trees and tall grass so how do i know for sure that there are coyotes in our area or should i go to my ungles house where he hears yotes and even shot a few off his front porch but wed have to use a shot gun (we have a 16 guage feather wheight and a 20 guage) because hes a big gun safety dude and theres houses by so where should i hunt at my house where i dont hear yotes and i can use a 243 or my ungle where theres yotes but id have to use a shotgun??