Just past the Bridge of the Gods you can find a Free public outdoor range. I think it is sponsored by Skamania County. Go out East on 14 and take first left just past Bridge of the Gods. Follow the signs after that.
It has been some timesinceI have been out that way though.
You can also shoot on Department of Natural Resources land (DNR). Yacolt Burn State Forest is an option. Out of 90,000 acres, you might find a place to shoot.