If you're on the westside, Santouka definitely deserves a visit. It's at Centinela/Venice in the Mitsuwa food court. <3 toroniku ramen.
On Sawtelle, Asahi Ramen and Chabuya tend to be the favorites. There's also Ramenya nearby on Olympic.
http://www.rameniac.com/ is considered the authoritative LA ramen guide. Give it a look.
11555 W Olympic Blvd, Los Angeles, CA 90064
3760 S Centinela Avenue, Los Angeles, CA 90066
2002 Sawtelle Blvd, Los Angeles, CA 90025
2027 Sawtelle Blvd, Los Angeles, CA