ok so here is "Male chases Girl first" tag results
https://mydramalist.com/search?adv=titles&ty=68,77,83,86&th=763&so=relevance
out of these i have seen
Koizora (a love story that will make sure you never forget it) The movie version is "sky of love" bitter sweet ending..took me 2 years to complete this 6 episode drama.
1 Pound no Fukuin while it is a boxing drama the focus is his love Sister Angela the Nun
Any of the Hana yori dango adaptions (BoF, Hyd, MG, MG18, MR, )
Pride - another sports drama that is a romance.
Boku wa Imouto ni Koi wo Suru --This one is difficult the acting is great but the topic--Twin incest--is VERY difficult to get past.
Say "I Love You" ahh the anime that got me into dramas--the movie is ok but if you love shoujo (girls manga) this is a love story that will melt your heart.
5-ji Kara 9-ji Made - A monk falls in love with an English teacher who just keeps running away from him. This one is priceless.
Sekai Ichi Muzukashii Koi - This is rom-com where the lead tries so very very hard to get the girl to like him but fails at almost every attempt.
I hope you find one that make you happy:)