Tony's and The Plaza (both right on Main St near the entrance to MK) and Skipper Canteen close at 7pm on party nights. If you can get a reservation at any of them between 6 and 7, you will be allowed to dine there, then be whisked out of the park after finishing...possibly out a back door off Main Street since there are parades and other party activities going on. Disney is pretty strict about private party activities being only for those with tickets.
Liberty Tree Tavern closes at 6pm on party days.
The restaurants that are open during the party like BoG, Crystal Palace, and CRT close reservations to non-party ticket holders at 5:55.