Cowboys and Indians, communists and ice-picks, Aztecs, artists, mariachis and masked wrestlers. We saw all of those, as well as colonial mansions, baroque churches, teeming markets and great museums.

We climbed pyramids, made guacamole and re-enacted human sacrifices. Then we went to the beach.

We had wanted to go somewhere hot and exotic with our two children, but not to have to spend ten days in a resort. We definitely wanted a bit of pampered, palm-fringed luxury at some point, but dragging the kids halfway round the world just to flop by a pool seemed wasteful.

I knew that Mexico, a vast and deeply civilised country, might provide the perfect adventure. What I didn’t appreciate is quite how intense that adventure would be from Day 1.

Mexico City is the sort of place that most people either avoid entirely or leave immediately. That’s a big mistake. This is one of the most tumultuous urban experiences imaginable, a monstrous megalopolis of about 23 million souls, too many to count, certainly, and almost all of them in vehicles that belch fumes and clog the roads.

But it is also one of the most exciting, rewarding and thoroughly cultured places on Earth. If you want your children to learn stuff on a trip, and take away memories that may even enrich them a little, then the city that Mexicans call simply Mexico is ideal.

We came armed with a long checklist to be crammed into our three days in town, and had a guide and a driver to help us to find our way through the insanity to our hotel – the splendidly trendy La Condessa.

First on our list was to check out the museums devoted to Frida Kahlo and Leon Trotsky, who were neighbours (and lovers) in a leafy quarter called Coyoacán. These museums are the actual houses where they lived, so they were small and personal with great stories to reveal.

We followed that by joining scores of Mexican families taking a floating promenade on the lake in Xochimilco. We boarded gaily coloured boats – they looked like big gondolas – bought food and drink from others floating by and then stopped a craft full of mariachis in their full regalia to serenade us.

After an hour sitting in honking car chaos we made it back to our hotel and rushed up to relax in the hot tub on the roof.

Next day was Aztec day. This entailed an early drive (before the heat and the madness) to Teotihuacán, an hour outside the city and one of the most impressive archaeological sites in the world.

Even our philistine offspring were slack-jawed at the scale and wonder of this place (especially when we climbed the giant Sun pyramid and volunteered Alfie as a sacrifice to ensure that the Sun would rise). They were even eager to go to the mighty Anthropological Museum, where the civilisation we had clambered over was placed perfectly in context and packed with pre-Colombian treasures.

There were more ruins poking up amid the charismatic mayhem of the Zócalo, Mexico’s tumultuous main square, where heirs of the ancient tribes don Aztec-style garb and dance for the crowds. Later, we had another side order of art as we took in Diego Rivera’s dazzling murals. We came for culture and we certainly got it.

Mexico City is exhausting and inexhaustible. We could happily have spent a week there but after three days we were also pleased to be on our way somewhere a little less frenetic. So four hours heading north in a luxury coach on open country roads, bound for the area known as Mexico profundo, was a dreamy interlude.

We went past sierras, arroyos, mesas and countless cacti, while cowboys on their steeds tended distant cattle. Eventually we arrived in a very different Mexican city. San Miguel de Allende, an elegant colonial Spanish enclave – all ochre mansions, cobbled streets, gabled courtyards and dappled squares – is unremittingly lovely.

It’s also manicured and mollified by the presence of plenty of affluent gringos shopping in its craft stores and sipping in its bars. Still, that didn’t detract from its sweetly Mexican charms.

Our hotel, La Puertecita, on the edge of town, was serenity itself: hanging gardens and translucent pools, and gentle, attentive staff. Time in San Miguel is sumptuous and slow. We began the morning with fruit and spicy huevos rancheros, ambled into town to shop and explore a church or mansion.

At lunchtime the kids frolicked by the pool and, after an early-evening saunter, we would dine in the city’s verdant square. San Miguel at night has a sensual, almost ethereal quality, with scents and sounds floating through the jacarandas.

To keep the culture quotient topped up we found time for a Mexican cookery lesson and visited a ranch, but we could have easily done nothing but marvel at the charm of this softly alluring town. And we could have kept doing that for a very long time – except that we had an appointment by the sea.

Whoever said “it’s better to travel than to arrive” has obviously never waited in transit at a Mexican airport for five hours with two bored and tired kids.

They were just about placated by the promise of a few sybaritic days on the Pacific coast. But even our high expectations seemed understated when we eventually landed in the province of Jalisco, on what has been dubbed the Costa Careyes.

The cacti had been replaced by palms and the hot air was heavy with tropical portent. The hotel, sitting alone on a dreamy sandy bay, was our vibrantly coloured, blissfully laid-back home for the next few days. The kids stopped moaning immediately. This was a shoe-less, stress-less kind of place – we had space and time and sunshine. Our chalky blue casita sat beside an azure sea.

The kids loved the infinity pool and the games room. I liked the margueritas and the lobster. My wife liked the intense terracotta colours and the massage. We all liked El Careyes Beach Resort a lot.

This part of the west coast of Mexico is sparsely populated and, thankfully, underdeveloped. Let’s hope it stays that way.

After all that culture I didn’t mind that we were isolated, because the staff and the ambience were still emphatically Mexican. Gentle, lilting, easy … beach resorts don’t get too much better than this. And nor do family holidays.