i want to know if is free

It depends on where you want to visit in the forest, as Angeles National Forest sprawls across a large swath of the San Gabriel Mountains just north of L.A. Some of the more popular recreation areas require you to purchase an Adventure Pass, plus pay facility fees such as parking. There's a link to a map showing areas that require fees in the forest here: http://www.fs.usda.gov/angeles. As for what to do, there are tons of great outdoor adventures to enjoy. GORP.com has some highlights here: http://bit.ly/K1YV1a, including hiking to the summit of Mount Baldy or taking on the mountain-bike trails of the old Mount Lowe Trolley line. It'll probably take you about an hour or longer to cross L.A. from Long Beach and get somewhere like the San Gabriel Reservoir in the forest. That's about 60 miles north of Long Beach, and I hear L.A. traffic can be a bear. Worth it for a day or two up in the mountains, though!