Andrew you have the key ingredients for sucess, one a spot were you know coyotes are, the desire to hunt them, and this great board with all of these members to help your learning curve.
Anytime you see coyotes, and if you see them frequent that usually means there is a good population. For everyone you see there will be several more in the area. Sounds like the area your describing is excellent habitat for them. I hunt alot of farm land here, there is feed for there prey along with plenty of water these places are magnets for predators.
If you want to keep the pelt wait tell your first freeze or so. By then they should have a good thick coat.
I have shot at coyotes in the past while passing through and they run off. I would then drive down the road about a 1/2 mile in the direction they went off too, and try calling them in. Lots of times they would come right in as well. This also works well when you spot animals and cant get shots. Just get down the road out of sight and start calling.
This time of year howling, and a coyote pu in distrees would probably be your best bet. The pups will be out on there own about late August - september.
Good luck on your next outings, I have a feeling your going to connect real quick.
Chad