Since wine is often consumed in the evening, it’s probably best to wait at least until the next day to nudge the user to leave notes (otherwise you might remind them in the middle of the night after they’ve fallen asleep, or first thing in the morning when they don’t want to be thinking about wine).
It sounds like the notes will help the user remember things about the wine in case they want to find it / buy it again, so you also don’t want to wait too long, lest they start forgetting what they liked about it.
Push notifications often get turned off when they’re not for important functions, such as sports scores or reminders to check into flights. Consider instead an in-app notification the next day (perhaps during the user’s afternoon or evening) that could say something like, “How was La Crema Chardonnay? Write some notes.” The notification could put a badge on the app’s icon as a subtle reminder.
If there’s an activity feed in the app, you could also put a nudge to leave comments there as well.