Unless there was supposed to be some other additions, Nyan's romance route has been finished for a while.
You need to talk to her about the enchanted clothing, complete the mini quest for that (beating Karl and Wolfgang) and report back to her. After that, she will freak out and close the shop for a day and when you go back, she will ask if you want to be her boy/girl friend.
Saying, yes will allow you to talk, compliment, give gifts, and flirt with her until you raise her affection enough, at which point you can ask her out on a date. You can only ask her out on Fridays or Saturdays AFTER 8pm.
Pay attention to what she says when you talk to her, she mentions things she likes, places she went to, or things she would do. When you go out on your first date, you will run into her mother, who cockblocks you, by asking you questions about those things and to be able to romance Nyan I don't think you can progress until you answer them correctly.
After all of that, you can take her out on a date every Friday or Saturday and I think you can fool around with her during the week, in her store.