set-up a candlelight meal
Dinner at an all night diner like Denny's. Dancing and drinks at an after hours club. Finish with a DVD, then watch the sun rise before parting.
Wow, sure if the rest of the date goes well. I mean, I have. Usually not on the first date. But I'm a guy, it's unlikely I'd say no to a woman I find attractive.
someplace that's open that late
Nowhere, I don't go on a date at midnight.