Four days in Yerevan: a pink city staring at a mountain it cannot reach

Start at Republic Square, which is the argument for Yerevan in one place. Tamanyan laid it out as an oval rather than a rectangle and specified the local tuff for everything on it, so five monumental buildings from the 1930s to the 1950s stand around you in bands of pink and cream stone with basalt trim, and the pattern of the paving repeats an Armenian carpet. It should be oppressive and it is not.

Then walk north up the pedestrianised shopping street to the Opera and on to the Cascade, which is the other thing everybody remembers. It is a stairway of limestone terraces climbing the hillside behind the city, begun in the 1970s as a Soviet monumental project, abandoned half built when the money ran out, and finished in the 2000s with a fortune from the American-Armenian businessman Gerard Cafesjian. The terraces are now an open air sculpture gallery, with Botero's fat bronzes at the bottom and escalators running up inside the structure past exhibition halls of glass art, Warhol and Chagall. Climb the outside rather than riding the inside, and stop at each level.

From the top, if the haze has lifted, Ararat is directly in front of you across the city. Come back down for dinner and stay out: Yerevan eats late and the whole centre is on the street until midnight.

Go to the genocide memorial first thing, and give it the morning. Tsitsernakaberd stands on a hill across the Hrazdan: twelve leaning basalt slabs closing over an eternal flame, and a forty four metre stele split down its length. It was built in 1967, when even acknowledging the deportations and massacres of 1915 was an act of defiance inside the Soviet Union, and the museum built into the hillside below it is careful, documentary and devastating. Allow two hours and do not schedule anything cheerful immediately afterwards.

In the afternoon, the Matenadaran, at the top of Mashtots Avenue under a statue of the monk who invented the alphabet. It holds something like seventeen thousand Armenian manuscripts, the largest collection anywhere, much of it carried out of Anatolia by refugees a page at a time. The display rooms show perhaps a hundred of them: illuminated gospels, medical treatises, the smallest manuscript in the collection weighing under twenty grams and the largest requiring two people to lift. Take the guided tour, which costs very little and is the difference between beautiful objects and a story.

End on the hill above the Cascade at Mother Armenia, twenty two metres of woman with a sword on a pedestal more than twice as tall, erected in 1967 on the plinth that had held a statue of Stalin until Khrushchev's thaw removed him. The park around her is full of Soviet military hardware and a slightly desperate funfair with a Ferris wheel, and the view over the whole city to Ararat at sunset is the best in Yerevan.

The best day out from Yerevan runs east into the Azat gorge and takes about six hours with a driver, which your guesthouse will arrange for something like fifteen thousand dram. There is a marshrutka to Garni but not to Geghard, so hiring the car is the sane option.

Garni first. A colonnaded temple in the Ionic order stands on a spur above the gorge, built in the first century AD when Armenia was a client kingdom balanced between Rome and Parthia, kept as a royal summer residence after the country turned Christian, and flattened by an earthquake in 1679. What stands now was reassembled from its own fallen blocks in the 1970s, which is why the joints are visible. It is the last classical colonnaded temple standing anywhere in the former Soviet Union, and the setting, on a cliff with the river a long way below, does most of the work.

Walk or drive down into the gorge afterwards for the Symphony of the Stones, a wall of hexagonal basalt columns hanging over the river like a cathedral organ, formed as lava cooled and cracked. It is a short and rough track from the village.

Then Geghard, ten kilometres further up the valley, where the road ends against a cliff. The front church was built in 1215, but the older and stranger part is behind it: chambers, chapels and a mausoleum cut directly into the rock, with columns, ribbed vaults and khachkar crosses carved out of the living stone rather than built out of blocks. Sound does extraordinary things in the upper chamber, and there is often a choir standing in it. The name means spear, for the lance that was kept here for centuries.

Armenia adopted Christianity as its state religion in 301, before anybody else, and this is where that happened. Echmiadzin, twenty kilometres west of the city, is the seat of the Catholicos of All Armenians and generally reckoned the oldest cathedral in the world, founded by Gregory the Illuminator on a spot where he said Christ had come down and pointed. The altar stands over what was a Zoroastrian fire temple. The compound holds the cathedral, the seminary, the residence and a treasury of reliquaries that includes the spear that gave Geghard its name.

Two of the churches nearby are more architecturally important than the cathedral itself. St Hripsime, built in 618 and named for a Christian woman martyred by the Armenian king before his conversion, is the model that Armenian church design copied for the next thousand years: a cross inside a rectangle, a dome on squinches, and almost no ornament. St Gayane, of 630, is the same idea worked out differently.

Then stop at Zvartnots on the way back, a few minutes off the airport road. It was an enormous three-tiered circular cathedral raised between 643 and 652, and it collapsed, probably in an earthquake, within about three hundred years. What survives is the ground floor: a ring of column bases, carved capitals with eagles on them, and the outline of something far more ambitious than anything else being built in Europe at the time.