I was the first customer in the door the day Amir's Falafel in Studio City opened in the early 80's. I worked around the corner back then and it was my favorite place to eat both falafel and the best schwarma west of Tel Aviv.
For the past 25 years, 15 of them living in Santa Monica, I look forward to any excuse to drive to or through Studio CIty so I can eat at Amir's. In addition to great falafel, schwarma, and kabobs - they have great salads and even the non-existant decor doesn't detract from the excellent food.
Amir's Falafel 11711 Ventura Boulevard, Studio City, CA - (818) 509-8641
Buddah's Belly at the corner of 2nd and Broadway should meet your requirements. A bit off of the Promenade is Fritto Misto at 6th and Colorado or Syrian food at Sham on Santa Monica Blvd. just west of Lincoln. Also consider Jinky's Cafe on 2nd just north of Broadway.