Agarest: Generations of War
This turn-based, Japanese TRPG uses a classic mechanical style similar to Final Fantasy Tactics, with great anime art-style and a blend of dating sim elements. Using a square-based field of combat, the game takes an interesting approach of using blind movements before combat begins, as well as a positioning system which allows for multi-character moves (similar to Kingdom Hearts except turn-based). This allows for a huge diversity of combat and strategies to employ.
Between combat, you’ll be adventuring though towns, exploring the very well-written story, and experience the dating sim elements. Using a moral choice system, your choices affect the way various characters interrelate with you. If you want a dating sim experience with great art, but with actual game elements, then this is your jam. This game can be extremely grind-oriented on higher difficulties, so those looking for a narrative-focused experience may want to tone it down a bit during their playthrough.