I’ll wait to hear more about the budget (i.e. UCLA in-state tuition only or UCLA tuition and room & board), but one school that popped to mind was Willamette. It’s in the capital of Oregon which makes it great for people interested in public policy, and it’s among a minority of liberal arts colleges that offers a major in public health. It also has a relatively popular major in Japanese Studies, should that be of interest to you. It would be a likely admit and also likely merit aid…the question is whether you would get enough merit aid to bring it into budget.
ETA: 40% of Willamette students study abroad and there’s a student newspaper and a literary magazine.