Four days in Guadalajara: the city that invented what the world thinks Mexico is

Start under the two yellow-tiled spires that are on every postcard of the city. They are not the original towers, which an earthquake brought down in 1818; what stands now went up in the 1850s and looks nothing like what the sixteenth century builders intended, which is a fair summary of the whole city.

Come out on the south side into the Plaza de Armas, where an ironwork bandstand shipped from France in the 1880s still has a band in it several evenings a week. Sit under the trees. This is what the centre is for.

In the early evening walk five minutes east to the small triangular square where the mariachi bands wait. Agree the price before the first note, expect the second song to cost the same as the first, and go while it is light: the streets immediately around it are not where you want to be wandering at midnight.

The state government building on the corner of the square looks like an ordinary administrative palace until you go up the main staircase. Orozco painted Miguel Hidalgo across the vault above it in 1937: the parish priest who started the war of independence, four storeys tall, holding a torch over a mass of fighting bodies, looking less like a national hero than like a man about to set fire to something. Entry is free.

Then walk east through the linked plazas behind the cathedral, past the fountains and the theatre, to the far end of the pedestrian strip. It is about ten minutes and takes in most of the monumental centre in one line.

The old orphanage at the end of it is the reason to give this day to one artist. Built at the start of the nineteenth century as a hospice, it is a low complex of twenty three courtyards around a chapel, and Orozco covered the chapel vault and dome at the end of the 1930s with a cycle on the conquest of Mexico. The figure in the dome, a man consumed by fire, is his masterpiece. There are benches under it made for lying flat on, and you should use them.

An hour northwest of the city the land turns blue. Agave grows in rows up the sides of the volcano here for as far as you can see, and the fields, the ovens and the old distilleries together are what UNESCO put on its list in 2006, rather than any single building.

The town at the middle of it is small, hot and given over entirely to one product: a stone church on the plaza, distilleries on the surrounding streets, and men selling cantaritos, the local citrus and tequila drink, out of clay cups in the square.

Take a distillery tour and pick one. The oldest maker in the trade has been distilling in the town since the eighteenth century and runs tours all day at several prices, the difference being how much you get to taste. Learn what reposado and anejo actually mean, then buy the bottle you liked at the source, where it is cheaper than at the airport and considerably better than what gets exported.

Tlaquepaque was a separate town until the city grew over it, and its centre has survived as a few pedestrian streets of low houses, courtyards and shops selling the ceramics the place has made for centuries. It is twenty minutes from the centre and roughly on the way to the airport, which makes it the obvious last morning.

Start with the pottery itself. The regional museum is small and free and lays out the local styles side by side, which is the difference between buying a nice souvenir and buying a good one an hour later.

Then lunch under the arches on the main square, where a covered hall of restaurants surrounds a bandstand and the mariachis work the tables from mid morning. It is touristy in the sense that everyone goes, and it is genuinely good.