The poem presents the feelings of a traveler who believes that she is a very different kind of traveler from most other people. Rather than stay in a guest house or hotel, she sleeps "in a local farmer's van." No one speaks her language, English, and she contrasts herself with other traveling "philistine[s]" and tourists, calling herself "an anthropologist in trunks."
The speaker uses apostrophe, speaking to someone who is absent or dead and cannot respond to her. When we see that the title is "Postcard from a Travel Snob," we might immediately think of the typical postcard sentiments like "Wish you were here!" Hannah creates irony by having her speaker say, in the very first line, "I do not wish that anyone were here." This line defies our expectation of what a postcard is supposed to say.
Hannah uses imagery in the rest of the first stanza, contrasting the peaceful place the speaker is in with "holiday resort[s]" that have "karaoke nights and pints of beer / for drunken tourist types." She has not gone to visit a "seaside-town-consumer-hell" that might call up a number of brightly-lit boardwalk scenes, with rides and games and funnel cakes for sale. Instead, she is isolated and happy about it.
The title tells us that the speaker is a "snob," and the poem seems to bear that out. She uses phrases like "perish the thought" to express her disdain for drunk tourists. She also seems eager to "assure" us that she is not a "small-minded-package-philistine-abroad." She calls herself "multi-cultural" and insists that she is friends with connoisseurs. She clearly feels incredibly superior to other travelers and, frankly, most other people.
The tone, the author's feelings about this person, seems rather judgmental, as though the author is mocking her and her sense of superiority. It's one thing to want atypical travel experiences, but it is quite possible to have this without casting aspersions on others. The fact that the author seems to expect us to understand that she judges this person (and wants us to as well) creates dramatic irony, as we know something about the character of the speaker that she herself does not realize.