In 2-3 days

You’d be mad to visit Mexico for a couple of days, unless you were merely transiting through Mexico City or ducking over the border from southern California.

If you are coming from San Diego, Tijuana is the main border town but it can be violent and dangerous — car theft and rip-offs are common. However, it does have plenty of nightlife to offer and you’d think every night was a Friday.

Mexico City is worth exploring in a couple of days. Stay around the vibrantly atmospheric Zocalo centre
for an introduction to this sprawling city’s monumental colonial
buildings and museums, such as the 16th century cathedral and Baroque
National Palace.Popocatepetl and Teotihuac‡n’s temples are must-do
day excursions, while you’ve also got to check out Lucha Libre, which translates as free fighting. The
WWF-style wrestling is second only in popularity to football and some
mask-clad stars have crossed over into politics, without even removing
their disguises. Also make sure you visit Zócalo. The municipal square
is the world’s second largest, after Moscow’s Red Square, and a cultural
melting pot.

You can also expect to be happily attacked by the city’s famous mariachi bands, who
play classic Mexican ditties for a bit of loose change, at the Plaza
Garibaldi. Marvel at the collection of pre-colonial artefacts in
the extraordinary Museo Nacional de Antropología, and take a day trip out
to the magnificent pre-Aztec pyramid (the world’s third largest, so
they claim) site of Teotihuacán.

In a week

If you have only a week in Mexico, you would be well advised to split your time between the capital and the Yucatán Peninsula. The peninsula separates the Gulf of Mexico from the Caribbean Sea and includes the states of Yucatán, Campeche and Quintana Roo. Put simply, the collection of dream-like Caribbean beaches and spectacular Mayan ruins, including a newly-crowned Wonder of the World (albeit unofficial), takes a lot of beating.

The recently-acclaimed Chichén Itzá is indeed well worth a visit, though there are other, less-crowded, sites equal, if not superior, in their appeal. Nearby Uxmal, for example, has less grandeur, but is superior in its enthrallingly intricate stone carvings (and the unnervingly large lizards watching you from the shade). Palenque, too, has a wonderful setting, surrounded by jungle.

In two weeks +

Follow the above itinerary but see even more of the Yucatan. Tikal, the most spectacular of all Mayan ruins as it stretches high out
of the dense rainforest, may be over the border in Guatemala, but is
also accessible on a day trip. Tulum, on the east coast, has some
relatively modest ruins, but it is more famous for its icing sugar
beaches and the see-through sea of the Caribbean. You can rent a beach
hut within yards of the gently lapping water and it’s a much better
option than the more famous resort of Cancun, a few hours north, which
is both overly built-up and busy.

Merida shouldn’t be missed either, if only to relax in the welcoming
plaza for a few hours. The peninsula is also famed for its Cenotes;
limestone sinkholes linked to vast cave systems and filled with
remarkably transparent freshwater.

Finally, consider flying to the southern, Pacific coast for stunning surfing beaches or making the trek to the Baja Peninsula for a taste of wild, remote and lonely stretches of desert and coastline that you won’t find anywhere on the more populated mainland.