Do I leave sets with out any action?

A week? A month? How long???

… are you seeing sign from critters you ain’t caught ?

A rat set? 3 days. A mink set? A week. Canine set? Weeks.

If you got other areas you want to set I'd say a week or two tops. If you aren't going to set new locations leave it set until your done trapping for the season. Remember your just beginning so what you do probably isn't going to be the same a top notch trapper that can roll in and clean out the majority of them in a week.
Just keep trapping and learning.

NTO
along this line---you need to keep in mind what is happening in your area. There's likely a localized dispersal from within family units that will be in play as seasons causes a shift from summer to fall coyote behavior and then there could be another longer distance dispersal that happens depending on your neck of the woods. You can skim the easy ones off the top pretty quick and things will often appear to turn dead with no sign etc. Part of the more technical learning game is figuring out where the shy and educated critters have gone once you have killed the easy ones, when the local dispersals happen AND where the movement of those pups takes place. None of that stuff comes particularly fast or easy for most. Keeping that in mind and that there will likely be dispersals at some point, you may be best to stay set and see what happens unless you have other spots lined up and need the gear. Not particularly uncommon in areas with pretty poor populations to have sets sitting for 3+ weeks with no takers.

3 weeks??? Chris that ain't trapping that's hoping....
Just messing with u