Pros: good powder snow, $40 lift tickets
Cons: BYOB, smaller sized mountain
Unless you know someone in Logan, skiers from other areas are not going to go to Beaver Mountain (the Beav, as it's called).
The Beav is about 25 miles NE from Logan, near the Idaho border (actually not near anywhere, it makes Snowbasin look like an urban area). What the Beav has to offer is good skiing, particularly if it's a powder day. They groom very little when it snows. It's a family owned resort and the lifts can be a little crowded on Saturdays and holidays.
For the experts, you really have to hit the back-country to find the steeps. Otherwise, there is good tree skiing and some fun terrain. The vertical is approx. 1500-1700. The Beav does have a few groomed greens, and someone of any level can enjoy themselves there (except an intense expert).
There is no lodging nearby, except in Logan, Garden City, or the back of your truck/car. No alcohol is served at the lodge. It is a very pretty drive to get there, but the road has it's dangerous spots. I've seen a number of cars wind up in Logan River when driving up U.S. 89.
Beaver Mountain is a fun day of skiing. And for 40 bucks, it's a good value.