Pacific Dining Car will probably be your best bet, as it's the nicest, but there's also...
25 Degrees http://www.25degreesrestaurant.com/
The Standard Coffee Shop http://www.standardhotels.com/hollywood/restaurants-bars/24-7-restaurant/
I would go to any of those on a date.
One day Mode may open again for a 24 hr French option...
Dinery options (given the KIND of date, I would say tese are at least ...options
Sam Woo's in Chinatown is open 24 hours
I think Sanamluang Cafe is open 24 hours....? or close to it?
Fred 62 http://www.fred62.com
Pipers in Koreatown (Western & Beverly
)242 N Western Ave, Los Angeles, CA 90004
BCD Tofu House
The Roosevelt Hotel has definitely become quite a hot, sceney place, which could be fun to take a date. But 25 Degrees has had quite mixed reviews on this board. It appears that a lot has to do with whether the head honcho is on duty keeping an eye on things and the staff on their toes. Otherwise, people have complained about the service and the accuracy of the cooking, which is supposed to be the focus there. And it is doubtful that the main person in charge will be there during the middle-of-the-night shift.
Of the list above, Pacific Dining Car is probably the only one that could be considered "nice."
Unfortunately, Tonny's in Pasadena is no longer open 24 hours.
There's a few other restaurants that are open very late -- Brite Spot in Echo Park and Swinger's on Beverly are open until 4 am. Bossa Nova on Sunset is open until 4 a.m. and might be ok for a date.
Several Thai restaurants in Hollywood are open until 4 or thereabouts, such as Sanamluang and Torung.