I really like the idea of Hit taking Frost out to do stuff after he frees Frost from having to hide on the streets.
Just.... the image of Frost actually feeling safe enough to let go and be able to relax, and him being able to enjoy himself thanks to Hit is so sweet to me....
Maybe they start off by going out to grab some grub at some places, since Frost would definitely need some better food after having to scavenge/steal, etc.
Him and Hit sitting together in a cafe sounds nice... maybe they talk or eat some sandwiches/desserts quietly, and Hit can't help but glance at Frost with curiosity now and again. But Frost just indulges himself, eating with enough manners to not look sloppy, but still visibly grateful to have good food access without the need to worry.
And for a moment... Hit sees Frost's potential to change into a better person...
And then later on, Hit might actually be generous enough to follow or take Frost to a theme park! And it would be like their first "date", hehe. Of course, Hit probably wouldn't be a fan of going on rides, but he may go ahead and sit on the Feriswheel or other, calmer attractions :)
In the end, him and Frost head home, Frost tired after such a thrilling time. He isn't ashamed to admit that he did have fun, because why else would you go to a theme park if it wasn't to do that?
Hit is just content in knowing Frost is in good sprits, having done his job for the day.