Plymouth, Utah? I grew up just a few miles south of there. The area right around there is mostly private property, and access can be pretty difficult to come by. Most of it is open dry/irrigated farm, open sage country, and some juniper. A few miles to the east is Cache Valley, that includes the Cache National Forest, there is some tough but good hunting over there. Deer is a draw every year,for both residents, and nonresidents. Elk is over the counter, spike or cow only in the archery season, there are some open areas in the state, where you can take any elk, but they are hard hunted. The archery season is short, gun seasons even shorter. Cache Valley, is also home to Culter Reservoir, super good carp shooting throughout the spring, summer, and fall, they can even be found during the winter.
Hope,this helps,
Thanks,