There are alot of roads/trails to the west of Bear Lake. Many of which are very scenic and will offer a great family outing. If you stop at the ranger station at the mouth of logan canyon they will give you an updated travel map for free. The great thing about the area is that all the roads connect. So if you wanted you could start at providence canyon and go all the way to bear lake. Vere little of the area though is challenging (sp) to any vehicle past stock. Providence Canyon is about the hardest place to wheel in the area and it is on the logan side of the mountains.
That being said, a trip to Mt Logan should be on everyones list of places to wheel to, and can be reached easily from the bear lake area via right hand fork, temple fork, or many other routes.