As for the previous reco's, I'd agree in this order: Bar Toscana (though it is Brentwood it has exactly what you are looking for), Copa D'Oro (only second because the food is really marginal but the best drinks in town and really interesting crownd without a pick-up vibe), Suite 700 (thrid becuase it can get cramped depending on when you go and the crowd is different every time I go), Angel's (because it is really hit or miss the kind of crowd you might get if there and later the live music makes it hard to talk), Viceroy (okay on all counts but just no terrific drinks/food--crowd all depends on your timing), Huntley (good not great food and cocktails but you will be ogled for sure if not approached--they go out of their way to have a certain kind of staff that attracts a certain kind of customer and it gets very busy early because of the sunset views) and Katsuya (last only becuase I don't think the drinks are anything special, they can have an attitude though not always, the bar itself is microscopic and if you want to stay for a while and not eat dinner it could get wierd...but unlikely anyone will try to pick you up).
The only place I would suggest against would probably be Katsuya, but you are likely to have a good time at most other places.
A couple other places to consider in no particular order.
--Hungry Cat in Santa Monica Canyon. Great food, great drinks, canyon crowd will not bother you at all.
--Bar Chloe. Around the corner from Copa. Very small but a cool, intimate vibe. Limited but good food. Great drinks. Crowd is unlikely to bother you, but can also be the problem...sometimes there is no one in there and sometimes it is packed.
--The Yard. Also within 100 yards of Copa and Chloe. Almost great food and almost great cocktails. More casual than all of the other places mentioned--there could easily be someone in shorts and flip-flops. Nonetheless, a fun easygoing group usually.
--Tasting Kitchen. This is actually in Venice but has great food, great drinks and a super cool crowd. However, it can get busy on a Friday night. You've missed first Friday but get there after about 6ish and finding a spot for four without having to stand/do musical chairs could get difficult.
--FIG. Great food and drinks. However, the only downside here would be that if the lounge area, which basically spills right into the dining room, is full, you can get stuck in the well, dining room. You might be able to call early tomorrow and get a table next to bar where it is more, loungey. Oh, you will definitely not get bothered here. Though the crowd can also be a total toss-up. Not bad, but it could be a lot of hotel guests.
--Wilshire. Right next door to Angel's. Has all the things you are looking for except maybe not that "interesting" of a crowd.
--Michael's. About a year ago they totally revamped their cocktail program and they now have a rooftop garden that the mixologist uses to source ingredients. The food will be very good. The only downside is that the lounge does totally feel like the 80's and is pretty darn small. However, the crowd is very ecclectic (okay, that means there will also be some people your parents age) and it is unlikely you'll be bothered. You are exactly who they are hoping to attract when they brought in Jason Robey at the bar.
Another way you could think of this is grouping certain places together so you can easily switch venues if something isn't exactly to your liking. Angel's and Wilshire are literally 20 feet from each other. The Huntley and FIG are probably a whopping 100 feet from each other and Michael's is maybe 150 yards away-one city block and change. Copa, Chloe and the Yard have front doors within 250 feet of each other. ShangriLa is about equidistant from both Fig and Chloe at about 2 1/2 blocks with FIG and Chloe being about 4 blocks apart. Bar Toscana could be coupled with Katsuya and from out of left field, Vincenti is just down the street. I didn't mention them before as a stand alone place because I don't quite think it is what you want, but the food is excellent, the drinks good and it can have a really interesting atmosphere--though the lounge area is small and it can get busy. Enjoy!
I would suggest Upper West on Pico. They have a great happy hour with amazing food, excellent wines by the glass and interesting cocktails. The lighting is really inviting and I generally find that the bar is easily accessible. The atmosphere is very relaxed, I have often engaged with interesting conversation, but never felt the "pick-up" vibe.
Another great happy hour is Copa d'Oro on Broadway and 4th. The best $5 cocktail in town.
Depending on your time - Katsuya or Bar Toscana in Brentwood, Bar Food in West LA, Angels or Wilshire in Santa Monica.
Closer to the water - The Huntley nice view or the roof top deck at the Shangri La (outside patio on the water basically). There is also the Viceroy. All have good ambience. And depending on time you can hit their happy hours, which are all very good.