If you are looking to get out of the hustle and bustle of this grand city (particularly during the stifling hot summer months), you may wish to consider a day trip.
The stunning Lake Balaton (central Europe's largest lake, flanked by long beaches) is well worth a visit, however, most people will probably find that it deserves more than just one day. If time is limited, take the train from Budapest to the picturesque town of Balatonfüred. The train takes just over two hours so it is worth setting off early and planning to get a late train back during the summer months. Balatonfüred is a spa town but also has some interesting shops and of course the obligatory cooling off opportunity at the lakeside beach!
Slightly further than Lake Balaton is the city of Pecs which will take close to three hours to reach by train (although it is in itself a beautiful train journey). Pecs is the fourth largest city in Hungary and is home to its oldest university which dates from 1367. The city is also home to the "Little Mosque" which is well preserved and serves as a reminder of the Turkish/ Ottoman rule in this region until relatively recent times. You can wonder at the beautiful almond trees which line the city's streets or visit the flea market which takes place every weekend. There is also an antiques fair which is well worth visiting should you find yourself in Pecs on the first Friday of the month.
Hungarian horsemanship is legendary. If you want to experience this, head to the Hortobagy Puszta region which is the "steppes" area surrounding Lake Tisza. Here you will find Hungary's best riders and displays of horsemanship which demonstrate the centuries of teaching and tradition that have gone into this most skillful of pursuits. The main areas for the tourist displays are Bugac and Lajosmisza. Check before you travel, however, as the towns host equestrian displays on alternating days. Bugac can be reached in just over two hours from Budapest by train and provides a very different experience from the bustling capital. Apart from the horsemanship, the Hungarian steppes are beautiful in their own right. .