Faith & Flower in downtown LA is a nice first-date spot - fancy enough but still casual. Gorgeous decor, amazing chef / great food, + inventive cocktails - their "Chief of Booze" is one of the best bartenders in LA. 

I also like Tavern Restaurant in Brentwood - another great spot with all of the above plus amazing desserts. 

Public School 310 is a great first date spot in Culver City. Great happy hour as well as beer and food menu. So is The Culver Hotel across the street.

I vote for El Coyote Mexican restaurant. It has been there since the 30's l believe. The food is authentic, and it has a full bar, but the margaritas are awesome. The Scratch one packs a kick. The food is good, the atmosphere is lively and there is a wide cross section of people there, young, old, artists, people in the industry etc. You can sit inside or outside on the patio where it's a little less noisy, best part is if you run out of things to talk about, you could always check out the others there and talk about them. It's always packed.

Versailles is also another good one that is not too pricey either. The food is good. It's Cuban, and they have generous portions.

Chin Chin is good. The salad is awesome, and you're right on Sunset boulevard so you can people watch, and maybe star watch/spot. Have fun!!!

I personally love Mercado Los Angeles, which has a few different locations, though I typically go to the 3rd Street location. I've also done some first dates at Eveleigh, though generally better cocktail menu than food menu, though the food is still good, too. Wildcraft Culver City is a good spot with good craft booze. 

Bar Ama is a fantastic choice!

Gracias Madre in West Hollywood is my go to. Great energy, a gorgeous outdoor patio, banging drinks and stellar food (and so that you're totally not thrown off guard, it's vegan. But like the type of vegan that a serious omnivore like me can't even help but love). Ask if Jason's behind the bar and tell him I sent you. His awesomely insane mezcal cocktails won't disappoint.

Laurel Hardware is cool. 

Ugh SOOO may places you could go! I think Cerveteca would be fun since its in the Downtown LA Arts district and from there you could either go grab a beer Angel City Brewery which is down the street or EightyTwo and have a drink and play pinball!

If your on the westside Acabar is a really cool middle eastern restaurant with awesome food (just note it can get pretty loud)

So many great ones. I recommend The Hudson http://thehudsonla.com/menu/

Blue Plate Taco in Santa Monica on Ocean Ave.  They have a really cute patio that looks out to the beach and the pier! Great tacos and margaritas :) 

Ford's Filling Station or Ugo in Culver City is great! and downtown culver city is just a cute little area in general~