Celadon (pan-Asian small plates), Chameau (Moroccan) and Carlitos Gardel's (Argentinian) are other fun first date spots in that area. Xiomara (Nuevo Cubano) might work, too--great mojito's but kind of an odd location.
7910 W 3rd St, Los Angeles, CA 90048
339 N Fairfax Ave, Los Angeles, CA 90036
7963 Melrose Ave., Los Angeles, CA 90046
6101 Melrose Avenue, Los Angeles, CA 90038
First date you want it to be vibey, but not spend too much, right?
Try Yatai Asian Tapas (www.yatai-bar.com)...a beautiful 30 seat restaurant on the north side of Sunset, just west of La Cienega. Lots of great sleections,a nd it won't break the bank...plus, it's got nice patio, too, if the weather is nice.
Angeli Caffe is my Go To
If you could get into Mozza, osteria or pizzaria, she might like that.
Uzbekistan is definitely "offbeat". Uzbek cuisine in an interesting setting. Take her to mashti malone's after for Ice Cream
Moun of Tunis is also fun, lounging on couches, eating moroccan food, belly dancers...hmm, good, but maybe too "suggestive" for a first date? I'd find it fub.