Hungary is a small country, so only a few hours of drive and you can visit even Vienna in Austria or Prague in the Czech Republic.
-As for Hungary, as long as the weather is fine, you might check out lake Balaton; the Norhern shore is quite pretty hilly and you can also take a swim.
-Szentendre is a small town situated just outside of Budapest and has a huge open-air museum presenting all of Hungary's cultural regions.
-The Hortobágy National Park is part of the world heritage because of its flora and fauna, and it represents well how the larger part of the untouched Hungary used to be once.
-Further places being part of the world heritage: Aggtelek, Hollókő, Pannonhalma, Pécs, Tokaj
-Some other pretty towns with notabel sights are Debrecen, Esztergom, Eger & Egeszalók, Gyula, Siklós, Sopron, Szombathely, Székesfehérvár, Vác, Visegrád.