I believe the establishment open the latest on property is Jellyrolls, a piano bar at the Boardwalk. It's open til 1:45am currently (could vary by season). I will caution, however, that the only food is popcorn and the drinks are nothing special. But the atmosphere and sing-alongs can be really fun (especially with a little pre-gaming and providing you don't have to drive). I've found it's very much like college in that it doesn't really get going until 9:30pm and later (after the parks close). The restaurants in the Swan and Dolphin within walking distance of Boardwalk are all open until ~11 or 11:30 (vs. the Disney restaurants in the area that close ~9:30) -- and are very good - Shula's bluezoo, Il Mulino. I think Three Bridges (open air bar & grill) over at Coronado is open until midnight. Think most Disney Springs spots are open until 11 - maybe 11:30 on weekends.
Playa Pizza is off-property, but in the MK area (can see fireworks through front windows) and open until 2am. Am sure there's a bunch more if willing to venture off property.