Date place near 3rd St?
On 3rd itself there's also Cynthia's with great food and vaguely romantic. Or 3rd Stop on the other side of La Cienega for a somewhat livelier vibe. Tasca is also a good suggestion.
Up on Beverly, there's also Terroni, and the new Della Terra which is still finding it's feet, but is in the House/Taste ballpark. BLD could work, though beyond breakfast I'm generally disappointed.
If you're willing to head up to Melrose, the Foundry may push you up to the next pricepoint, but if you sit in the lounge area and order small plates to share, not really. Ditto Vinoteque next door. Otherwise Village Idiot is decent, when it's not too packed. And there's the new Melgard Public House in the old Louise's space.
One last option...though it is undeniably "in a mall"...once you're inside the Whisper Lounge on the edge of the Grove, you're very much in House/Taste territory as well.
Haven't been to either of those, though I did look at the House menu and it looks great. Have you checked out BLD? We've been there for all three, went to dinner for Dine LA and it was wonderful. Reasonably priced, somewhat innovative food and very nice date atmosphere I thought.