"within the city" can be a bit nebulous given that late night transit without a car can be sparse;
but Eat-n-Park locations are open with food service until 11 two hours past 9.

Another option that is a bit more outside the box:
Planet Fitness. They have free wi-fi. a membership is like $10 a month last I checked and they are open 24 hours M,T,W,& Thurdsay into Friday at which time the close at 10pm friday night (weekend hours are tighter). They have locations in the city.
and while some have vending machines for snacks and beverages, no real food options.

I could be wrong but if you're a member, I highly doubt they'd bat an eye at you using their seating area up front (every one I've been in had one) and as a bonus, as you took breaks, you could actually go work out for 15 or 20 minutes.