It is FREE to visit Hancock Park and the La Brea Tar Pits. There is a fee for the museum. Metered parking is available on 6th Street or on Wilshire (9 am to 4 pm only, read signs carefully). Paid parking is available behind the Page Museum off Curson, or in the LACMA garage off 6th Street.
Definitely take some time to walk around the mall. It's quite large, but I'd recommend heading over in the direction of the capitol, or going over to the Lincoln Memorial and Vietnam Memorial area.