This sounds similar to Mariya Takeuchi’s Plastic Love. It’s kinda strange hearing someone sing Korean within the Japanese City pop genre but that’s probably cause Yukika is Japanese (:
She's reminiscing about the times she shared with this one person. She wants to be alone, and is comfortable with it but as the night goes on she becomes more restless and lonely. She looks at the neon lights, realizes she's alone, and is comfortable with that fact once more. She's reminiscing again as she looks at the lights, hence "can't take my eyes off you." The whole song is about the struggle of missing a past relationship, while being alone in the present.