From a shaded table on the roof garden of the Majestic Hotel, one can dine or just have a martini and look down to the world's second largest square, la Plaza de la Consititution, known to virtually everyone as the Zocalo.

It is an awesome sight. The Zocalo has been the political and religious center of Mexico for more than 600 years; only Red Square in Moscow is larger. They say that everything that is Mexico and Mexican either originates in this city or finds its way here, and the core of it all is the Zocalo.

There is nothing plastic or neon about the view, no signs for Holiday Inns or McDonald's. On the north side of the square is the magnificent Catedral de la Asuncion de Marcia, the Metropolitan Cathedral, constructed over a period of 250 years beginning in 1573. The cathedral, the largest church in Mexico, has 16 chapels and 27 altars, reflecting the most popular architectural styles of three centuries.

The National Palace, dominating the entire east side of the Zocalo, was constructed at the end of the 17th century to replace one once occupied by Montezuma, ruler of the Aztecs, and later by his conqueror, Hernando Cortes. Cortes took the city known as Tenoch-titlan in 1521, after three months of fighting, turning Mexico into a Spanish colony for the next 300 years.

There is enough architecture, history and culture in the Zocalo and immediately around it to keep an inquisitive tourist busy for at least a week, and so it is best to first make a fundamental decision about where you want to stay in Mexico City, the old city or the new.

I chose the Hotel Reforma on the Paseo de la Reforma, nearer to the Zona Rosa -- Mexico City's more modern center for nightlife, restaurants and shopping -- than the Zocalo. The Reforma was one of the city's deluxe-hotels several decades ago and is a comfortable place now undergoing renovations where rooms start at about $35 a night. But if and when I do it again, and it is definitely an experience worth repeating at greater length, I would head for either the Majestic or its neighbor on the Zocalo, the Gran Hotel Cludad de Mexico. The Gran's prices are comparable to the Reforma's; the Majestic's are more modest, starting at about $18 a night. tNeither is classified as deluxe.

The Gran is an outstanding example of innovative hotel conversion. It is at 16 de Septiembre No. 82, in turn-of-the-century building that was once a fashionable department store. The belle epoque lobby is huge and elegant, with a Tiffany-like, inlaid glass-ceiling and delicate filigree wrought-iron elevators at either end. I could not resist riding one of the gilded, open-cage elevators up to the open balconies that surrounded the lobby, then walking down the steps to admire the murals of old Mexico City on the walls.

Like the other cities of the world comparable in size -- Tokyo, London, Moscow, Shanghai and New York -- Mexico City is what you make it. If you want museums, there are more than 100, and one nobody should miss is the National Museum of Anthropology, generally acknowledged as one of the world's greatest. It's open daily except Monday, from 9 a.m. to 7 p.m.

If you like parks, try Chapultepec, especially on Sunday when traffic is curtailed and families take to the streets. You can visit Chapultepec Castle, which, over the years, has been a fort, a palace, the home of Mexican presidents and now, the National Museum of History. Or, a few blocks from the Zocalo, visit the Alameda and its monument to Benito Juarez, who united Mexico against the French intervention of the 19th century.