Musashiya has excellent udon. Everything else I have tried (tempura, kara age) has been poor.
http://www.yelp.com/biz/musashiya-udon-noodle-los-angeles
Many folks on the old board praised TLT (the brick and mortar operation of the lime truck). I found it OK in a “greasy gourmet” way. Only one visit - never felt like a return, which is not a great sign.
http://www.tltfood.com/home
Just out of the Village is Ramen Yamada-ya which has both excellent ramen as well as kara-age.
http://www.yelp.com/biz/ramen-yamadaya-los-angeles