Sounds awkward to me: sits onto the balcony.
Yes. Even the hungarian sentence is incorrect.
Az idős orvos kimegy az erkélyre és olvas. - The old doctor goes out onto the balcony and reads.
"Az erkélyre ülni" is also correct. Maybe more commonly used as "kiül az erkélyre".
Hmmm..... I pictured someone sitting on the edge of the balcony. Or maybe a large balcony with a chair on it. Couldn't that be a possibility?
I got a solution but it was wrong in Hungarian "Az idős orvos ül az erkélyre és olvas." Possible solutions may be these: "Az idős orvos ül az erkélyen és olvas." or "Az idős orvos kiül az erkélyre és olvas."