What are good cases with good airflow that support a 160mm Fan under $70 CAD

Solution
none.
160mm isn't a computer case fan size you'd commonly find anywhere.

120, 140 and 200mm are the common fan sizes.
95 and 80mm on the small end.

Unless you meant CPU heatsink height.
These cases will support 160mm heatsink:
https://ca.pcpartpicker.com/product/3MPfrH/deepcool-case-tesseractsw
https://ca.pcpartpicker.com/product/CkM323/cooler-master-masterbox-lite-5-atx-mid-tower-case-mcw-l5s3-kann-01
https://ca.pcpartpicker.com/product/FtV48d/corsair-case-cc9011051ww
https://ca.pcpartpicker.com/product/hygPxr/deepcool-dukase-v2-atx-mid-tower-case-dukase-v2
https://ca.pcpartpicker.com/product/JcgPxr/corsair-270r-atx-mid-tower-case-cc-9011106-ww
none.
160mm isn't a computer case fan size you'd commonly find anywhere.

120, 140 and 200mm are the common fan sizes.
95 and 80mm on the small end.

Unless you meant CPU heatsink height.
These cases will support 160mm heatsink:
https://ca.pcpartpicker.com/product/3MPfrH/deepcool-case-tesseractsw
https://ca.pcpartpicker.com/product/CkM323/cooler-master-masterbox-lite-5-atx-mid-tower-case-mcw-l5s3-kann-01
https://ca.pcpartpicker.com/product/FtV48d/corsair-case-cc9011051ww
https://ca.pcpartpicker.com/product/hygPxr/deepcool-dukase-v2-atx-mid-tower-case-dukase-v2
https://ca.pcpartpicker.com/product/JcgPxr/corsair-270r-atx-mid-tower-case-cc-9011106-ww
 
Solution