FYI, it might be a little crowded out on the trails. Lots of things going on during the 4th of July in Big Bear. The village and lake get especially crowded. Then there is the fireworks show, which launches off of a barge in the middle of the lake. Whatever you decide, you'll have lots of company :beer:
Really depends on what you have in mind. Big Bear has a wide range of trails for all levels. Do you want hard rock crawling? Or some easier stuff?