After an awful lot of searching online I came up with the following coordinates:
Kaán Károly kilátó (Károly Kaán viewing tower), 47°32’0”N 18°57’18”E
Makovecz Imre kilátó (Imre Makovecz viewing tower), 47°31’47”N 18°57’58”E
Do these look correct? I have looked on Google Maps, but the image quality is too poor to be certain. I am asking because I would not want to get there only to find that the coordinates were wrong. Also, there is some conflicting information online and I would like to know that I have opted for the best information. For example, there was this page, kirandulastervezo.hu/celpont/… which gives coordinates for Clark Ádám tér!
How popular are these with tourists? There doesn't seem to be much information online. I got the information from the Hungarian website for the Children's Railway (http://www.gyermekvasut.hu/wp/latvanyossagok) and also an English webpage on their website, which gives a rather abbreviated version: www.gyermekvasut.hu/english/page.php?4. I guess the assumption is that English-speaking visitors have less time on their hands and only want to see the highlights.
I may have some more questions later, but that's all I have the stamina for at the moment!