Near the Roxy...
at Sunset/Doheny for Sat. eve. Not sure what is close by (5 mile radius) Been to Doughboys already...What about The Golden State???
Good food a must (I know, can be relative), burgers ok, not more than 50$ total for two (we don't drink) Coming into "town" is always special for us so, open to suggestions. May entertain two separate places, one for dinner the other dessert.
Amarone Kitchen and Wine is great Italian and very close.
Talesai is dressed up (non-Thaitown) Thai food: I would say that it is really good if you don't know real Thai food, but only average if you do.
Yatai, Asian Tapas, is adorable with good pan-Asian treats, a nice price and nicer patio. Bar Marmont isn't that far and worth a look-see if you have time and Pinches Tacos is right across the street.
Oh yea - the infamous Rainbow Bar and Grill is right next door to the Roxy. Walk in, have a drink and checkout wild pics and memorabilia of the Sunset Strip's rock n' roll glory days. They have a greasy, heavy pizza that one of my friends just adores, I'm not a fan of it at all. I do enjoy their fresh fish and chicken dishes far more than I care to admit as a foodie/chowhound.