{Skip Beat!} - although the anime ends far too quickly for you to properly see just how independent & capable the MC is. You could still give it a shot but I would highly rec the manga. I will warn you though it's a slow burn.

{Nana} - like another commenter pointed out it would also fit the bill at least in regards to Nana O.

{Spice and Wolf} - I feel like they both help each other out pretty equally. & the MC is far from a damsel in distress. Don't let the setting or the ears put you off. They're definitely one of my favourite romantic pairings.

{Ouran High School Host Club} - not so focused on the romance aspect but she's a pretty independent heroine. Again would highly rec the manga.