It looks like a rental car would run you around $50 for a day in the LAX area.
Google Maps will give you directions using public transportation options, but it gives you a route that takes about 4 hours on a Saturday morning. It’s still going to cost you $15-$20 minimum, so a rental car quickly starts to look attractive.
You should post up a new thread asking for a ride once you know when you’ll be in town. Maybe you’ll get lucky and find someone willing to give you a lift.
Another option would be to use public transit on say Friday to come down to the area and stay a hotel nearby. There’s a few options that are within walking distance for under $100.
You can try airbnb.com and couchsurfing.org to find inexpensive accommodations.