Does anybody know how to visit a/some caves of the Caves of the Aggtelek and Slovak Karst from Budapest by public transit?

There are two daily buses from "stadionok" bus terminal (caution! it's NOT the central bus terminal at Népliget). You can get to the terminal either by metro (red line) or with tram No1, The daily departures are 6 15 and 7 30. Arrive earlier as you have to buy the ticket beforehand in the ticket office or in a vending machine. The terminal is not that big, there is a signboard that shows the nest departures - you bus will go to JÓSVAFŐ, there you will see which stand it departs from. The buses arrive at 10 43 and 11 18. Get off at "Aggtelek Kossuth utca, Barlang bejárati út (Kossuth str -way to the cave). This is the last stop before the Aggtelek bus terminal. From there take Kossuth str, (I'm quite sure that there will be some kind of signboard.). The entrance is cca 900 m from the bus stop. If you go in September take the 7 30 bus and you can reach the 12 00 tour. From October 1st the tour schedule changes, so you should take the earlier bus and you can reach the 11 30 tour. This is the short, 1 hour tour. Alternatively you can try to go - with the same bus - to Jósvafő and get off at the Szálló "Hotel" stop. As the entrance here is very close to the bus stop you have (LOW) chances to reach the 11 00 tour in September. Don't do that in October, as there is only one tour from Jósvafő entrance at 16 00,.

There are two buses back also 14 37 and 16 30

All other sites are in Slovakia, and they are not doable on a daytrip from Budapest by public transport.

Thanks for the detailed description! Do I get it right the bus takes almost four hours to get there?

joycevs Yes. It's quite far, and the bus has several stops. It does not take the motorway all the way it could, as it serves some minor setllements.

joycevs In fact it's four hours and forty minutes.

Ah, I guess I have to skip it for the upcoming trip then, I'm sure my retired mom is not going to sit on a bus for that long haha. Too bad, it was my only Hungarian WHS still missing

joycevs If you can drive, rent a car for a day. It's much faster so. You can be there within three hours. You can take the motorway up to Miskolc (m3 - m30).

Only visited the Aggtelek cave in Hungary, but visited most of the caves in Slovakia. It's very difficult to access most of them by public transit, your best bet is to rent a car and drive yourself. As ajoszucs said, there's a motorway up to Miskolc and then it takes another hour and something to reach the border area where the cave is located.

Should you decide to visit caves in winter, Aggtelek is fine, open most of the time, but for Slovakia, most of the caves are closed and only couple stay open, so check beforehand when and how can you visit (usually only by guided tour).