I visited Hungary in 1990 and lived there 1991-2003.
Of course, the changes came gradually. But here’s what it was like my first year there.
In eastern Hungary I visited a village where there were 4000 inhabitants and only 20 telephones. A distant relative of mine lived there, and I had to send her a telegram [!] from the post office to let her know I was coming.
Even in Budapest, the capital, there were plenty of people without phones. My girlfriend was one. To get in touch with her, I had to go to her apartment in person and, if she wasn’t in, leave a note on her door asking her to call me from a pay phone.
Major landmark buildings were covered in decades of soot, or had decades-old scaffolding around them. Major buildings had shrapnel damage from World War II, or bullet holes from the 1956 revolution.
The local currency, the forint, was not convertible, and locals were permitted to purchase only a very limited amount of convertible currency (dollars, deutschemarks, etc.) So there was a black market. For one dollar you could get 62 forints officially, or 90 forints in a furtive transaction in the back of someone’s shop.
There was already a McDonalds in 1990, but Burger King arrived later, around 1992, and was treated like the Second Coming. KFC and Pizza Hut came around the same time.
Some goods were hard to find (like shoelaces) and some goods impossible to find (like peanut butter). Budapest was like a ghost town on Sundays, as not only shops but most restaurants were closed.
I remember one corner grocery store selling shoes side-by-side with eggs.
I remember paying about 8 cents for a photocopy of one sheet of paper and getting a carefully handwritten invoice for the transaction.
Compared to the economic changes, the political changes were far advanced by 1990. But early on, it wasn’t clear if democracy would survive, or if the communists would come back into power, or some form of right-wing authoritarianism would come back [spoiler alert: it did]. The Jewish community worried about a resurgence of anti-Semitism. Meanwhile, there were still Soviet soldiers marching around the train stations.
To answer your question, I’d say that most of these quirks were gone by the mid-1990s (in Hungary, at least! As Banksiaman notes, each country was different).