Summarize:

[Note: This only works on Tuesdays, and not in winter]  Buy a Casteliacone for ₽100.  She will buy your Casteliacone for ₽2000.
Go to Castelia City. Walk up Mode street, which is the second from the right. Talk to the last person in the line for ice cream stand. Go to Nimbasa City and exit through the upper-right exit toward Driftveil Drawbridge. Enter the parked caravan/trailer and talk to the girl inside.