All of WDW is family-friendly. My DH and I did a monorail crawl in October (without the kids) and we've tried to eat a number of times or have a drink at some of the bars/lounges (with and without kids). I think the biggest challenge of the lounges is waiting for a seat. My experience is that the waits can be long and some of the lounges have very limited tables and the bar seating can be awkward for families.
Here is what I can report:
1) The bar seating at The Wave is extensive, but would have been awkward for a family. I think there's a lounge area, but not sure if they have waiter service. Seems that it's used mostly to have people wait to get seated at The wave.
2) Trader Sam's had an hour wait (which we waited in our room).
3) Mizner's was completely full. Not a single seat at any of the few tables or at the bar, so we actually left without trying it.
4) We struck out twice trying to get a table at Territory Lounge for 4 while staying at WL. Full every time.
5) Victoria Falls (AKL) is mostly bar seating, although they have some 2-tops along the balcony.