Okay, polarizing opinion, I adore Lwaxana Troi. She's generally treated as an annoyance, by basically everyone, but she's probably not only one of the most well-rounded individuals in the Federation, she's also incredibly powerful. But my favorite thing is how Picard reacts to her.
This man, who has dealt with Klingon Terf Wars, Romulan Spies, Anomalies of every kind, heck, he was even Borg for awhile, somehow completely falls apart around this woman. With everyone else he exudes quiet authority and dignity, you just kind of automatically respect his presence. Lwaxana Troi doesn't give a shit, she knows her own worth and power, she's more involved in living than work, she sees people as they are, and not who they are pretending to be. If she was evil, she'd be the greatest villain Trek has ever known, but she has better things to do, ruffling the feathers of powerful men, and a bit of hedonism is much more interesting. I want to be her when I grow up.