LUKE: No, no, no, uh, what I meant was – ah, what the hell? Would you like to have dinner with me sometime?
It’s pretty obvious that, besides being flattered by Nicole’s attention, Luke asks her on a date primarily because he knows Lorelai is dating Alex. Jess has already criticised Luke for waiting around for Lorelai like a faithful dog, and has nagged him to ask Nicole out. Finding out that Lorelai is out on a date with a coffee shop owner who’s outdoorsy and likes fishing (sounding suspiciously similar to Luke) is the final straw that pushes him towards Nicole.
In this scene we learn that a cup of coffee at Luke’s cost seventy-five cents. That sounds like a bargain for what every character seems to believe is the best coffee in the world.
Notice that in the background to this scene, someone walks behind Luke and Nicole wearing what appears to be a maroon and gold Gryffindor scarf from Harry Potter.