@pdhopeful I am currently not a student but went through the grad app process last year when my wife and I lived in Florida. I admire your optimism. Although, this is my second round with AFI as a pruducing applicant (second interview as well) I too always try and have an optimistic disposition.
After I was rejected last year from 7 schools (although I interviewed at 2) my wife and I packed up and headed out west. So to answer your question, in my opinion, there is really no point in searching for housing until maybe late June. Realistically, when a prop manager or landlord posts and ad for an apartment they are typically looking to fill it within the month.
I would recommend, however, fimiliarizing yourself with neighborhoods via research and average rent prices in those desired.
Again, from my experience in scouring LA for a decent place to live we noticed that it's a dog eat dog world out here. Meaning, if you find a place you like in your price range that feels right to you, be prepared to make a down payment on it IMEDIATELY. I am talking minutes not days. My wife and I found a place in Franklin Village the first day we visited. The landlord recommended we go get a check from the bank to secure the place. No more than 45 minutes later when we returned it was snagged by another couple.
We ended up finding an apartment on Los Feliz Blvd. about a 5 min drive (if that) from AFI. I remember before we moved here people telling us that we just wouldn't be able to afford the rent or trying to make it sound way worse than it actually is. Don't let anybody scare you about this. There are plenty of viable options for housing at fairly reasonable prices. We were lucky enough to have a friend live here a year before we moved that really helped us. If you have any specific questions about neighborhoods, sources for finding apartments, or anything else please feel free to message me. I would be happy to answer and questions.
Hey who knows, if we become fellows together maybe I could help with the search.