It wouldn't be too bad. No great holidays in June but if it's in the end of June, there might be the beginning of the summer holidays for students. So the train would be very crowded. Better to book the tickets in advance. For train, normally you wouldn't get any discount so no matter when you book it, you'll get the same price. And the flight? hmm... still suggest you to get it in advance. But talking about the peak season or not. From the end of April, the peak season came, and will last to the end of Oct, from the perspective of tourism...