Parking is hit or miss. If you can't get parking directly in the main lot, continue up the hill and turn right onto University. You usually can find a spot there, and walk down the steep trail.
Or, if it's after hours, I think you can park across the street in the doctor's lots. There's actually a large number of office buildings back there, including my opthalmologist, Dr. Basham who rocks. He weilds a mean laser for cataract surgery or detatched retinas.
So, back to the park. What I love is going on the Billy Jones Wildcat Railroad. It's not a long trainride, so it's good for very young kids. But it's just fun. And then there's the restored carousel. Who doesn't love to feel 7 years old again on a horsey going up & down to carnival music?