Another vote for doing something fun- at the very least, bring a board game, or like my cousin used to do bring a Taboo deck in your pocket for emergencies. Or a crossword puzzle, though if you think there is anything you’re not “supposed to know,” remember not to fill it in. (This has happened to me, but then again I do have a really disturbingly broad pop culture knowledge that I kind of wish I didn’t.) But if you do know something random, it can lead to interesting conversations.
I vote a museum, personally. It’s formalish enough that nobody’s scandalized about not being in a lounge anymore but also can be a lot of fun.
Or a nice park, especially this time of year, unless you’ve got my allergies in which case snuggle up in a blanket with tissues and wait til July.
Interesting conversation was never inspired by a lounge, unless you’re both the people-watching type, in which case I grant it can be very interesting indeed.