The UCLA classics department is great; I am in the classics Post-Bacc program there and took a bunch of classics courses as an undergrad. I love it and hope that I don't have to leave!
Living in LA is a huge issue though, I paid $1365 for a crappy single close to campus back in 2006 and I have friends paying $1600 now for a crappy 1-bedroom close to campus (they have two people sharing the bedroom and one person using the dining room as a bedroom, so rent is $533/person). I now live about 25 minutes away and the rent is only $850 for a 1-bedroom, but it takes 1 hour to get there during the morning commute. However, if you're ok in a bachelor with a sink and hotplate, it's about $850 to live 10 minutes away near Palms.