While not under $20k, the Subaru Impreza and Crosstrek are currently offered with a stick shift on the base trim, and for the Impreza Sport ($23k) it's offered standard with a stick, and an auto optional.
This may change soon to only be the WRX and BRZ with a stick shift next year, but currently their lineup is rather competitive for AWD compact cars.
This may change soon to only be the WRX and BRZ with a stick shift next year, but currently their lineup is rather competitive for AWD compact cars.