Walk-in-purchaseでいいのでは・・・

都市から国への移動、しかもダイヤ改正(12/10)を控え乗車日の記述なしでは回答に窮します。まずはハンガリー鉄道で現行の時刻表をご確認下さい(12/10以降は目下表示なし)。
http://elvira.mav-start.hu/elvira.dll/x/index?language=2
・ハンガリー鉄道で乗車券予約購入の場合、取扱い駅(Ticket collection points)で乗車券と引換が必要。(e-ticketではない)。無札乗車は罰金。
Passengers travelling without a collected ticket must purchase a new ticket on board and pay penalty.
・ハンガリー鉄道はいわゆる早割の概念がない
・国内線の特急は座席指定料が必要だが国際線は料金に含入。寝台を除き空席に座ればよい。
・Budapest-東駅は国内線と国際線の窓口が別(変更されているかも知れませんが･･･)
・往復割引がある
　1. If you only want to embark on a return journey, buy a return ticket for a given destination
A return ticket is worth buying for those who make a journey to a given location and return, and do not plan any other journey. (Passengers wishing to roam in Europe or in the vicinity of the given destination, should find out about our rail passes.)
It is good to know that the following are also international return journeys,
•if the outward and return journeys take place on different routes,
•if the return journey does not start from the destination, but from another station
•if the passenger does not return to the station where he departed from.
For example, the following are international return journeys:
Outward journey: Budapest – Stúrovo – Bratislava
Return journey: Kosice – Hidasnémeti – Budapest
1. 1. Return ticket price reductions on the railways of Central-Eastern Europe
MÁV-START has agreed with several railway companies of Central and Eastern Europe that a big discount from the normal international ticket price is given in the case of a return journey. (Example: one can make a return journey to Romania with a 50% discount.)
Have a nice trip!