Yes. In 1983, by plane, car or train. You could fly into the airport- that was simplest. By car, you were timed between checkpoints, the assumption being that, if you took too much time, you might be picking up a fugitive. Train wasn't hard- passports were checked on board, that's all. It was also possible for American tourists to visit East Berlin- you could watch soldiers still doing something scarily close to a goose-step.

Any info I could provide on what they thought of us would be anecdotal.