Most CA schools actually do fly you out. And yes, it's usually coordinated with their Admitted Students Day. Stanford and Boalt are the two that flies the most people out (in fact, my friend at Boalt insists they offer this to ALL admits, and I have not yet verified this... though they do fly out a huge number for sure). UCLA flew me out and put me up at a hotel for 3 nights, and reimbursed me for all expenses including any food or taxi fare I incurred. So I know UCLA does it, and I hear USC does the same for some of its applicants. The only other schools where I've personally known people who have been flown out is Chicago and Georgetown. Keep in mind though that aside from maybe Boalt and Stanford, most schools only fly out a small number of people, so don't expect it... but enjoy it if you get it.
I've also known people who got flown in free after calling the admissions office and explaining to them how much they'd like to attend the admitted students day but have financial issues so they can't afford a plane ticket. So might as well call and try if you're serious about a school. Use your discretion though. Funds are usually limited and trust me, you'll feel very attached to these schools because they treat you so well. Makes saying no that much harder.