Shiraz: 19 staff, students and lifelong learners from Edinburgh College of Art tip off the Tehran flight. Wafts of rosewater in the terminal, a scented warm breeze and the sound of the evening call to prayer suggest this art study tour will not lack sensual appeal.
Shiraz glitters as lights come on, people mill about, enjoying the wide spaces of this 18th-century urban masterpiece. Presumably stony-faced mullahs and anti-western hostile Iranians will be encountered tomorrow.
A rose garden and reflections from a turquoise pool, shimmering on the eaves of a decorated pavilion, characterise our mesmerising first Persian garden. Also visiting are schoolgirls. Lots of them. We learn the important questions. Where are you from? What do you think of Iran/the headscarf/marriage? By teatime, slightly embarrassed, we have become Madonna - autographs, photographs, being mobbed. Repressed Iranian womanhood is presumably in hiding, along with the mullahs.
But at the theological college, the mullahs are there, reading the Koran in the courtyard. A tentative request to photograph five mullahs, sitting on a wall, produces lots of smiling, an invitation to join in. Even Reza, the guide, is astonished. Lots of snaps, addresses (and prayers) exchanged. Presumably it's the stony-faced mullahs' day off - these chaps are charming.
Persepolis: Alexander (who was not Great - the Persian view) did terrible things here. Shattered columns, vast platforms and bull-headed capitals rise dream-like from the desert, while crisp detailed carvings of Darius's tribute-bearers holding lion cubs survive intact. There is excruciating embarrassment at the guide's polite, steely "now in the British Museum". Incredibly, there are no other tourists.
Firuzabad: Ruined 4th-century palace, a creamy mass of domes and arches, glassy sacred pool, snakes, frogs and scarlet dragon flies. Like figures in a Piranesi, we disport ourselves elegantly among the ruins, eating dates, feta and walnuts. No one else here either. We meet migrating Qashqhai nomads. More questions. What do we think of Iran society? And Israel? Do we understand Iranians like Americans, but not their government?
To Yazd, via another picnic in a 17th-century caravanserai (medieval motels for camel trains). Through purple mountain ranges so fabulous that whenever the guide says "photo opportunity" we catapult off the bus, dazzled by the landscapes. This is truly the Arabian Nights.
Yazd's soaring tiled minarets are beacons in the old quarter, dwarfing the wind towers that catch the slightest breeze. Serious shopping opportunities arise: woven textiles, 18th and 19th-century quilting, ditto blue and white ceramics, rugs, tiles.
Esfahan: Add to list of world's top five must-see places. Superlative architecture, stupendous blue tilework, exquisite paintings, a spectacular congregational mosque and, as elsewhere, delicious fragrant delicate food. Apart from a couple of busloads of French and Germans, still no one else here.
Attend a gymnasium ritual recalling Persia's defeat by the Mongols combining ancient poetry, prayers, some disorganised mock heroic wrestling and an undeniably decrepit keep-fit display: imagine Freemasons doing aerobics while reciting Chaucer to baffled Peruvians. Weird - except here, it's to do with an embattled, ancient Persian past and strangely affecting.
Tehran, then home. Iran is magical and captivating. The West's obsessive fear of Islam and equally mad oil obsession inhibit the tour companies' "Islamic experience" and this is a massive benefit to world culture. The taste of a ravishing past alongside an intriguing, hospitable, largely unwesternised present, and there is no one else there. It's so great not even the Scots miss the booze.
Geraldine Prince is director of the Centre for Continuing Studies at Edinburgh College of Art.