Westside for eight
the price point is tough, assuming you want a sit-down kind of nice place, but...
Maybe Cha Cha Chicken on Ocean in Santa Monica if Jamaican is okay
Jack'n'Jill's in SaMo
Gaby's Mediterranean in Venice
in case you were open to Japanese instead of Chinese, there's Musha in SaMo as well, tho I fear that would break your price point as well
Criteria = Westside, under $20 p/p, seating 8 together, Not Loud, & No Mexican, Chinese (*), or Persian.
Assumptions = Would prefer No Chains, not American (i.e. simple burger place), and something with some ambiance:
Italian - Westwood Village - Mio Babbo ~ Their prices are not on their website; however, based on a 3 year old menu, I count 32 entrees (that all come with house soup or salad) under $15. I think they can seat 8 in the round table by the window, or they can push tables in the center together that can easily accommodate 8 (check middle picture):
(*) accendentally put Italian origanlly.
When you say "under $20 pp" is that after tax and tip (what about drinks?)?
Depending on your "final" budget you could consider http://www.lagrandeorangesm.com/
Another fairly inexpensive place in SM for your group would be Fritto Misto on Colorado.
601 Colorado Ave, Santa Monica, CA 90401