Pretty much every moderate and deluxe resorts have a lounge and some of the nicer restaurants have lounges as well. Disney Springs has a lot of options like the Coke rooftop and Jock Lindsey’s Hanger Bar. Unfortunately, Jellyrolls at the Boardwalk is still closed with no opening date in sight. Just to let you know though, kids are allowed pretty much everywhere in Disney, including bars/lounges, aside from a few places that aren’t open right now.
If you’re wanting a more adult experience, you might want to head off property. There’s a really cool place near UCF called Cloak & Blaster if you are geeky at all.
To add to the list from @Random Ninja - Phinns at the Dolphin is a bit more upscale and more of an adult experience. I'm not sure if Abracadabar is open yet at Boardwalk but that would be a good spot for an adult beverage or two as well.
Trader Sam's Grog Grotto at the Polynesian could be a good place also (although I think it's still closed) There are rarely any kids there and in the evening (8?) it becomes adults only. There's not really any seating so I have seen several strangers share a table or stand by the bar together.