Kaeru no Oujo-sama is a good drama and also very underrated. If you're looking for something musical and uplifting, I really recommend it. It's not incredible or amazing or anything, but it gave me a very satisfied feeling after watching it, if that makes any sense.
Legal High is fantastic if you're looking for a comedy. Both Aragaki Yui and Sakai Masato are wonderful in it, they play off each other so well. Just be prepared for some really ridiculous cases!
Marumo no Okite is pretty good if you're looking for a family drama.
The
Trick series is long but very funny (and ridiculous). It has three seasons and several specials and movies. I'm not sure if it would be up your alley, though. It has a pretty specific sense of humor that people either love or don't.
Out of what's on your PTW list but doesn't fit your criteria, I just wanted to say that
Kazoku Game is absolutely AMAZING. However, only watch it if you are in the mood for a very serious drama. It has superb writing and a wonderful cast.
Piece is good but again, pretty serious. It has romance but the most interesting thing for me was the mystery.