During your stay in Hungary of course you should also schedule a visit to the capital Budapest.
By train you can ride almost every hour to Budapest for around 6 € / person.
Current timetable of the Hungarian State Railways.
One must expect about 1.5 hours for the train journey to Budapest Deli pu (South Station). NOTE: With the slow train it can take up to 3 hours from Balatonföldvár to Budapest.

If you want to explore Budapest on your own you should already 2-3 days plan to see everything. There are also guided tours you can book cheap in a travel agency here at Lake Balaton. These are i.d.R. by bus and often last only 1 day. Ideally, these excursions as a tour guide explains everything and you do not have to walk on foot to all sights.
Budapest is the seventh largest city in the EU. More infos about Budapest.

Recommended course are also multi-day bus tours to Budapest. More information can be found on the homepage of the tour operator MedkurTravel Bt

If you are traveling on your own in Budapest, it is advisable to take a taxi to visit the various attractions. The taxi ride is affordable and you will have no problem with finding a parking space. Take action, so that you experience no unpleasant surprises later still before driving the price of.

If you are traveling with your own car, you should (as in all big cities) always remove all valuables from your car to avoid nasty surprises. By car it is about 135km from Balatonföldvár to Budapest.

It is in any case advisable to plan the itinerary in Budapest in advance otherwise you can pretty bogged down with time as the traffic in Budapest extremely messy.