Roles and success
There is irony in Goethe's successful role as an authority in his community and in various academic and political institutions. He has attained something, but is it happiness? It is accomplishment. The things that make a person suspect happiness, like power, success, respect, and accomplishment, are all suddenly seen by Goethe as irrelevant and unnecessary when he departs into nature. In nature, he is just another animal moving through space and time, and he finds that his quest for self is unique when he is journeying.
The hero self
Although Goethe understands technically, his journey from home into the wilderness and back again matches the archetypal motif of the hero's journey, Goethe sees this as irony, because he isn't any more or less heroic per say. It is as if what the journey really does is allow Goethe to see an aspect of himself that isn't obvious when he is embedded in his daily life and reality. It isn't that he "becomes" a hero, but that he sees himself doing the hero thing, perhaps. The irony is subtle, but he notices it and talks about it.
Internal and external journey
There is an intrinsic irony in Goethe's view of travel. On the one hand, he is subjected to many new sights and experiences throughout Europe. But, on another hand, is the goal of his travels to experience some new external reality? No, on the contrary, Goethe's diary proves that he is primarily concerned with experiencing something new and dynamic in his internal experience of self. There is a strange synchronicity between his ineffable experience of self (symbolized by the diary source material) and the external reality of Italy.
Death and the sublime
Goethe's own opinion about this publication is that, to him, it was all literally true, and it was a sublime supernatural experience. This irony is poignant, because it involves his consideration on his own death. The reality of daily life is so busy and rhythmic that perhaps anyone would get sucked into the illusion of it, but while traveling, there is nothing to consider but Goethe's own experience of life. He adds new days of experience one at a time, but that only serves to illustrate the way life works, one day at a time, until what? He knows the answer of that question and this lends an ironic darkness to his "vacation."
Memory and regret
Another ironic aspect of these journeys is regret. Why should walking around Italy make someone feel deeply nostalgic and regretful? Perhaps one answer is that this is not Goethe's first rodeo, so to speak. He has been traveling through life the entire time he has been alive, but his regret is ironic still. The poignant intimacy of nostalgia is well-noted in the journals, but without answer. Something about living life in a circumspect, intentional way makes Goethe sometimes overwhelmed by the weight of his own experience.