TL;CR

TL;CR MEME
1. Comment with your character.
2. Receive comments from others.
3. Reply to their comments with long ballads and explanations of your characters' relationship throughout the game.
4. Endure everyone else reading your comment like the vultures they are.
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Becks do you remember when you crashed into my disco and you were like DO YOU WANT OUR IDIOTS TO HOLD HANDS SOMETIME BECAUSE I THINK THATS WHERE IT WENT DOWNHILL
If we're being honest I THINK Kaoru decided somewhere around week 2??? that he actually was attracted to Miki. Prior to that they had CR and she was fun to tease and play with and he liked mocking her but slowly he started recognizing it as flirting and just kept doing it. For Kaoru, Miki was very much a Haruhi stand-in at first not even so much because of Haruhi herself, but that's the sort of person he's attracted to. People who are practical and don't take his bullshit but still let him goof off (see: Haruhi, Kyoya, Miki.)
I think when she was setting his leg and they were talking about home also really solidified that he cared for her because he started seeing her as someone very strong and capable who could use someone else to rely on instead of doing everything herself. After that, he started lingering around and doing what he could for her (making her med bag, doing research, etc) and generally trying to get to know her better instead of seeing her as personal entertainment. He set up the dating café 50% for his own amusement and 50% because he wanted to channel his romantic feelings somewhere because he wasn't actually sure she'd ever reciprocate.
They've talked about this, a little, and some of his self-esteem issues but he wasn't actually sure she would like him because he thought she'd view him as an airheaded rich kid which would've been fair. Again, it's the Haruhi effect but without the everyday exposure like Haruhi got he wasn't sure it would grow on her and he had zero reason to try. A lot of the reason he did eventually tell her and kiss her is because Lili's a bully and he knew that pushing the Lili/Kara agenda meant he should at least...try.
Even now he's still not entirely sure why she likes him but he's absolutely endeared to her and will hold onto her for as long as he can? He isn't the type to change his personality for someone he likes so he'll still be a host and still be a devious brat, but he's more consciously putting her best interests ahead of his and keeping her feelings in mind.