Quiet Lounge in Santa Monica or Brentwood?
It's really going to depend on what your per person price threshold is. Wilshire Restaurant on Wilshire Blvd. along the eastern edge of Santa Monica comes to mind (especially the patio) but the cost could be an issue for a first date.
2454 Wilshire Boulevard, Santa Monica, CA 90404
I like Nook, in the back corner of a minimall off Santa Monica Blvd. east of Barrington. The two-tops along the wall are close enough so you interact if neighbors are seated alongside. Great food, not too expensive. Great choice -- if my date saw the strengths of Nook, we'll get along.
Nobody's mentioned the Penthouse, in the Huntley Hotel on 2nd in SM, not for food, but drinks are good and the view is killer, especially if trying to impress. If they press you to book a table, you can always just order apps, not that expensive.
Casa del mar has a pretty hotel lounge, again, not inexpensive, tho. I would also second Wilshire, nice patio.
Also, Whist at the Viceroy on Ocean is gorgeous, and I believe you can get a table on the patio for just drinks.
Chloe or Copa d' Oro, are my top choioces for quiet lounge; both near second street in Santa Monica. Vincenti in Brentwood has a nice bar that is almost always quiet. The W hotel lobby bar tends to be quiet earlier, and the Palomar is a good choice too. I also like Wilshire, but it is really dark for a first date. Arsenal's patio is good earlier, if the weather is nice.
12008 W Pico Blvd, Los Angeles, CA 90064
11930 San Vicente Blvd, Los Angeles, CA 90049
1449 2nd St, Santa Monica, CA 90401
217 Broadway, Santa Monica, CA 90401