The Flying Pig restaurant in Little Tokyo is going ahead with anime nights every Thursday. There's nothing in LA happening like that. The last Thursday of every month has a costume contest to look forward too.
Check their Twitter for what will be playing, there's suppose to be an updated site down the line with more info on the weekly event.
Anime Night at the Flying Pig Cafe
in Little Tokyo
6pm-10pm
141 S Central Ave Los Angeles, CA 90013