My DH and I always look for stuff to do once the parks close. We like heading to the Epcot resort area (Yacht Club/Beach club/Boardwalk). We like the bar in the Boardwalk, ESPN Zone, Yacht Club has a ping pong table near their maragarita bar that fun. We've also just wandered around the hotel lobbies to see what they look like.
We stay at Port Orleans French Quater, and really like the guy that performs there nightly. There should be a link somewhere of where live performers are. Are you staying on property? Maybe check out if there's anything going on there at night. Also, we like to hang out in the jacuzzi at night - there's less kids.
Downtown Disney, we like Raglan Road. Try a Snake Bite, wicked good (hard cider, beer and black currant). They also have live music inside or you can sit at the outside bar. We also like eating late at the Rainforest Cafe then darting in to the stores right as they are closing.
Polynesian has beautiful grounds. It's been recommended to us to get a drink at the bar and walk around the grounds in the moonlight.