Where do coyotes like to travel? I know roads are often use but where else? Do they run along water? Creeks?

Look for tracks, they are pretty good indicators of travel. U can't learn everything on the internet.

Check edges
Like woodline along a field, fence bordering farm field, along creeks that border fields

Places coyotes like to hunt, fields, pastures, grown up fence lines

Watch some youtube videos and then get out and look for similar places

X2. Railroad tracks, river bottoms, lake edges, ridges and such. If you get and snow, get out and follow their tracks. You can learn alot by doing that.

any kind of edge. field changes, corners, farm roads.

i always try to set on sign, but i always set these kind of places even if i dont see any sign.

i have a lot of places i catch coyotes every year where i rarely see sign.

Missouri is different from PA but scout any farms with cows or other animals, creeks that cut through any fields, & check out power/pipelines.
Scout these & similar places after a snowfall.

Any pinch points that you hunt for whitetails is usually a good start.
Also look for the path of least resistance through or around the super thick stuff.
Prevailing wind should also be considered as well
But I'm not a big coyote trapper. I just don't have that big of a population