Since I've never really looked into it I sort of just assumed that Churchill's "Iron Curtain" was this impenetrable wall that strictly kept the West out of the East. But a recent article on Reddit about an Italian porn actress who was born and raised in Hungary who worked in a hotel frequented by Americans has made me question that idea.
Was there a large degree of travel between the east and west? Was there still a sense of the "commonality of Europe," despite the political divides? Would it be normal to have, say, a Polish family move to Germany?
The main reason for the Iron Curtain was to limit the exodus of Eastern European citizens to the West, not the other way round. We have to discern between the states, though. Albania for instance was very much off limits for almost everyone. The GDR had a huge problem and lost thousands of workers and intellectuals before the Wall the built - so the Wall was basically a means to limit the brain drain of the GDR.
The was some permeability in sports - Good athletes were allowed to travel to championships in the West, but were kept under close surveillance. But looking at the other way around, the Eastern Bloc states were very interested in inviting athletes to their competitions.
Sorry for being anecdotal, but my (Austrian) girlfriend often traveled to Hungary, Bulgaria and the Soviet Union for figure skating competitions. And she easily visited ice rinks in the closer vicinity (Bratislava, Brno) for practice every week.
A Polish family simply moving to Germany would be an exception, although many Poles (Wikipedia quotes 700,000) left the country during martial law in the early '80s. They would not have been able to sell their possessions or take much with them, so you'd rather call them (political) refugees than just a family who moved.
Tourist travel from western Europe to the east was pretty common. Yugoslav beaches, Bulgarian ski slopes, Hungarian spas etc. offered cheap holidays to the more curious or adventurous (especially if one took advantage of the currency black markets).
In theory every country was open to tourism and had a state-run tourist organisation, but some were easier to access than others. Yugoslavia and Czechoslovakia, for example, offered visas on arrival. Non-Germans in W Berlin could travel into the East for a day without visas (via Checkpoint Charlie).
Independent travel to the USSR was possible, but in practice it was far easier and cheaper to book a ‘package tour’ through Intourist, the govt. agency.
Albania was the most difficult to enter, with tourism very strictly controlled and limited.
Edited to add: 'Once Upon a Time in the East' by Dave Rimmer is a very funny account of tourism behind the Iron Curtain. I think it's out of print, but it might be worth checking ebay.