Cedar Point is almost exactly between Detroit and Cleveland (I think it is slightly closer to Cleveland - I would recommend going to Cleveland - you can take in the Rock and Roll Hall of Fame in addition to Cedar Point - and Cedar Fair (Cedar Point's parent) owns and operates Geauga Lake which is near Cleveland - It is not great, but another park to check out if you have the time - Part of it used to be Sea World of Ohio - I could lament about that for hours, but I digress).
From LAX, you could take Northwest nonstop into Detroit or Continental nonstop into Cleveland. That said, you would probably do better cost-wise if you take an airline affiliated with the alliance you are taking over from Australia. NW and CO are both part of SkyTeam. If you are flying Qantas, they are oneworld. In that case, you would probably get a lower fare taking an American Airlines flight to Chicago or Dallas and connecting into Detroit or Cleveland.
It's definitely going to involve renting a car since either way is still about an hour+ away from CP. Unless you want to do Greyhound, and the cabs to get from the airport to the greyhound station and the cab from the Sandusky Greyhound to any hotel near Sandusky is going to be double the cost of the greyhound ticket (been there done that...)
That said, I usually fly into Cleveland.
"Tonight I wash my hands of you
You set the bar I could not live up to
Tonight the light is breaking through
So thank you very little and send me postcards from hell"
I live here in Ohio and yes your best bet is to fly into Cleveland and rent a car. The drive to Sandusky to Cedar Point is only about an hour from here. I'd allow yourself two days to do the entire park.
As someone else said Cleveland is also about an hour from Cedar Fairs other Ohio park Geauga Lake. It is a decent amusement park also with several good coasters worth checking out. It's probably a one day park if you skip the water park portion.
Now if your really motivated and have a couple more days you can drive about 4 hours south and catch Kings Island also. Another decent amusement park.
Cedar Point though is the best of the three by far. Good times to go are late May and early June as well as late August and the September & October Hallow-weekends where they decorate the park for Halloween. Some of the rides are closed though in the fall so I would recommend the spring to avoid the big crowds. If your going during peak summer time I would allow three days to see everything at the park. Good luck and hope your trip works out!