PS, to add to my first response
I'm not against him going on dates. Dude deserves a harem of women and dates every other day. My issue is the timing. At least have the date in the same city if it was that important or take his mom and sister with him. Dude went to a whole other country. He should have learnt from last time his sister was attacked and he had used up his shadow exchange. Any thing can happen, especially with a giant gate hovering on top of his city that's far from normal.
I think the date was still in Korea? And Jinwoo, believes on his ability to teleport. It was also hinted many times in the chap that Jinwoo could fly real quick to anywhere. So yeah, he is still alert. Probably went there cause he is confident he could travel as fast as he wanted. He learned from his sister's incident so he haven't used his shadow exchange yet so meaning he could do it anytime now. And if teleport doesn't work it was hinted many times, he could use his dragon shadow to travel fast.
Regarding the timing, I think it's fine? If you really think about it. He thinks, he'll probably end in a dire situation or something. So he wanted to invite the person he's interested to for a date. A person who he never had the chance to make a move with or anything cuz he's always busy with everything. He might as well have one date before dying or something. He's still a grown man. I see nothing wrong with taking a break before dying situations. Man only wanted a break.
If he through he would die, wouldn't our MC, the one we know and love go and spend his possibly last moments with the people most important to him? His family?
Through the series he tells and shows how his family is the most important. Heck he became a top hunter because he wanted to help them. All the progress was for them. So why is he miles away from Seul with a girl he barely knows (yeah he barely knows her, we can count on finger the amount of interaction they have and in all of them, he never showed any real interest in her). If they really wanted a love interest, a good one. Healer girl from the start of the series. They had history together. They had chesmitry together and if I remember correctly, he showd interest in her. They could've used their relationship to heal her trauma from being a hunter. They both could've been great influence on each other. But the author simply decided to put 2 hottest characters together and have them smach literally minutes away from the war.
If he truly believed that then why not take his mom and sister too? That huge gate could be dropping a nuke on his country l for all he knows. Between hunting down hunters and not obeying the games rules of the gates, the monarchs have already proven to be unpredictable. He could like a 100 girls, he had every right to, but this was not the time. Imagine if your country was going to war but your army decided to take a vacation instead as the enemy break your borders. He knows the monarchs are hard to beat, it's not like other hunters can handle them whilst he rides on a magic caper around the world!
The date is in Japan, not Korea. He's not in Korea. Whilst he was clearing the giants in Japan he came across a spot of nature he liked, that's where he took her. Also how can he so sure, it's the monarchs we are talking about. You'll see the consequences of his little rom com trip, not to mention spoilers - but if he has stayed in the same city a lot of bad things coming in the next chapters would have been avoided..
I think you wanted more romance drama than the author wanted. I thought you don't like romance in action series. I'm confused. If author went with that healer. It's would mean more romance drama than Cha Hae In route. Author wanted to make more actions and just peak romance.
And yeah, he literally did a lot of things for his family. So maybe he can have a day for his self. Like spend it for his other personal wants. I think he deserves a day for a lil date. Cha Hae In is important to him too so yeah. But yeah, if you really think this ruins ALL the goods things author gave us, then it's up to you. It's your taste anyway. I just think it's fine in my part.

In the novel i hated this part. Jin Woo literally knows there's a war coming, a huge mysterious gate opened, top hunters are getting executed and we have monarchs who can create pocket dimensions that are hard to detect but he goes on a freaking rom com trip! Like, can he be serious?