There are a few tour groups that offer guided tours of the "Gold Fever Trail" up Van Dusen Canyon to the old site of Belleville mining town. Instead of paying $30 a pop, go to the Big Bear Discovery Center, pick up a self-guided tour map of your own and head on out (if you're car can handle the drive up- 5+ miles each way of dusty dirt road). There are numbered stops on the way for the "Hanging Tree" (not the real one), a miner's cabin, Ross's Grave, Pygmy Cabin and such. Its a bit of Big Bear history that most people don't know about. Some of these sites are A LOT more fun at night when you can scare the caca out of people!!
There are acres and acres of forest and mountain to explore all around Big Bear. There are fantastic views of the valley and lake from the top of most of the peaks. The Big Bear Discovery Center and/or the Ranger Station is probably a great resource for established trails but venturing off on your own path has it's rewards. Make sure to buy an "Adventure Pass" from either place mentioned above if parking on Forestry land so you don't get ticketed.