Ocean and Vine in Santa Monica. Their Large space can accommodate large parties. I had a very good dinner there last month. They also have a fun firepit where people can hang out and gather before dinner. Very good mixed drinks. I was there on a weekday, so it was pretty empty/quiet. Not sure what it would be like on a weekend.
Can I ask about your concern about noise level? I would think that one wouldn't mind, and perhaps might even prefer, a rather boisterous atmosphere for a 21st birthday.