Bowling is good for an activity. Bars, of course - it's fun to go around to different bars and find one that suits you. If you can find a jazz club, especially the one where musicians go after their jobs, that'll get you thru the night in style.
Truck stops are great. Some of them have all-nite fun things like arcades, etc. Late restaurants. If you're REALLY late, bakeries start operating at like 3 or 4, bang on the door for early samples.
We used to go to the laundromat to hang out. Usually quiet, machines for soda and candy, we could hang out and not get hassled. Even put a few quarters in the dryer for heat on those cold Ohio nights.
You can take treats to the police station and the fire station. The emergency room is usually too busy for the staff to accept goodies, but worth dropping by to check.
Some motels, usually the really nice ones, have an all night staff person. You can hang out in the lobby if you're nice to the staff person.
I assume you don't want to go the the grocery store/7-11 and read the labels. I used to enjoy that, but it isn't much of a date activity.