Ten days in Portugal: one railway line, and every stop feels like a different country

A tiled terrace on the way up, looking over the Alfama rooftops to the Tagus. This is the view most people have in mind when they picture the city, and it is free.

People have lived on this hill since the 8th century BCE and fortified it since the 1st, through Phoenicians, Romans and Moors before the Portuguese took the city in 1147. The walls are largely rebuilt, but the ramparts hand you the whole of Lisbon at once, and late afternoon is when to be up there.

Walk down rather than waiting for a tram, and eat one street back from Rua Augusta rather than on it.

The high point of Manueline architecture, paid for by the spice trade and built through the 16th century. The two-storey cloister is the reason to come, carved with ropes, corals and navigational instruments. Vasco da Gama is buried in the church next door, which is free.

The original Belém bakery is a few doors along. There is always a queue at the street window; walk past it and inside, where several rooms of tables move much faster.

On the water across the road, a stone prow crowded with the figures who sailed out of this bay. Go up for the view down onto the compass rose laid into the square below.

The riverside cafés are fine and unremarkable. The cooking improves two streets inland.

Ten minutes west along the river, built in the early 1500s to guard the harbour mouth and said to be the last of Portugal that departing crews saw. Inside is small and the stairs are one narrow spiral, so entry is metered and slow; the outside is arguably the better half.

About forty minutes. Go early: the hill is quiet first thing and full by midday, and that difference is the whole character of the day.

A Romantic fantasy in yellow and red, raised in the 1840s on the ruins of a monastery by a king who liked pseudo-Moorish turrets and could afford all of them. The interiors are the royal apartments, left much as the family had them in 1910. Tickets are timed.

Along the ridge from Pena on foot. Walls the Moors began in the 10th century, running the crest with nothing but forest below. Less inside than Pena and a far better view of it, plus most of the coast on a clear day.

Come down before eating. There is very little on the hill and it charges accordingly.

An estate bought in 1697 and rebuilt at the end of the 19th century by an owner with money and an interest in secret societies. The grounds are the point: grottoes, tunnels, and an initiation well you walk down in a spiral of nine turns.

The convent church whose roof came down in the 1755 earthquake, on a morning when it was full for All Saints' Day. It was never rebuilt. Gothic arches stand open to the sky over a floor of stone, with a small archaeological museum at the end.

Ten minutes north at the top of the Glória funicular, a terraced garden along the edge of Bairro Alto with the castle directly opposite across the valley. Take the funicular up rather than the street.

Ten minutes uphill from the garden, and the neighbourhood where Lisbon eats well without queueing.

One oil magnate's private collection, left to the country and displayed in a low modernist building in its own garden: Egyptian relief carving, Islamic ceramics, Rembrandt, and a room of Lalique glass that people come back for. Two hours is enough and the garden is free.

About an hour and three quarters on the Alfa Pendular. It stops at Coimbra-B outside town, so allow ten minutes more to cover the last couple of kilometres into the centre.

Founded in 1131, and the burial place of Afonso Henriques and Sancho I, the first two kings of Portugal. Romanesque underneath and Manueline on top after centuries of rebuilding. The cafe attached to it, in the former chapter house, is the best-looking place in town for a coffee.

The lanes between Santa Cruz and the river, tight, tiled and full of students. No particular route: this is a wander before dinner rather than a sight.

Founded in Lisbon in 1290 and settled permanently on this hill in 1537, which makes it one of the oldest universities in continuous operation anywhere and a World Heritage site since 2013. The Joanina library is the set piece: three baroque halls of gilded shelving, kept free of insects by a resident colony of bats let out at night.

Student prices are the rule in the lanes below the university, and the portions are built for people who have just walked up a hill.

A national collection of sculpture, silver and painting in the old bishop's palace, built on top of the Roman forum. The vaulted galleries underneath it are the surprise: a preserved Roman substructure you can walk through, dating from when this was the town of Aeminium.

Two minutes downhill, a 12th century Romanesque cathedral that was built to double as a fortress and still looks it, with a Renaissance doorway added later. The cloister is quiet in the late afternoon.

About an hour from Coimbra-B to Campanhã, then a local train the last few minutes into São Bento. Stop in the entrance hall on the way out: the walls are covered in painted tile panels of Portuguese history.

A small neo-Gothic bookshop from 1906 with a crimson staircase curling through the middle of it, and one of the most photographed interiors in the country. Entry is ticketed and the price comes off a book if you buy one. Go late in the day rather than midday, when it is shoulder to shoulder.

Two minutes away, and 226 steps up a baroque bell tower to a platform barely wide enough for the people on it. The view along the gorge explains the whole shape of the city, and it is best in the last hour of light when the granite turns gold.

A 13th century Romanesque cathedral that looks more like a keep than a church, which is roughly what it was. Baroque decorators worked it over later and lined the cloister with blue tiles. The terrace outside is free and holds the whole river bend.

Drop down through the lanes rather than the road. Ribeira is the row of tall narrow houses along the quay at the bottom, the oldest lived-in part of the city and the middle of the World Heritage area. Touristed, loud, and still what you will remember.

The tables directly on the waterfront charge for the view. One street back and up the steps the same plate costs noticeably less.

Uphill on the Gaia bank, one of the oldest of the British-founded port houses, with a terrace looking straight back at the city. The tour explains wood ageing properly and the tasting is not stingy. Book before you leave the hotel.

The 19th century merchants' exchange, built over the ruined cloisters next door to persuade foreign traders that Porto meant business. The guided tour ends in the Arab Room, a ballroom of gilded Moorish plasterwork that took eighteen years to finish. Tours only, in rotating languages.

Next door, and the better of the two. A plain Gothic shell whose interior was later buried under carved and gilded woodwork, vines and cherubs over every surface. The catacombs below are part of the visit.

Porto's own dish: layered meats under melted cheese in a beer and tomato sauce, usually with chips banked around it. Have it at midday, where locals eat, and plan nothing strenuous afterwards.

A white concrete polyhedron dropped on a square by Rem Koolhaas, all sharp angles outside and warm plywood inside. Guided tours run daily and the acoustics of the main hall are the reason the building is shaped the way it is.

The city's traditional produce market, reopened after a long restoration, with fish, fruit, cured meat and cheese under an iron roof over two levels. Buy something to take home from the stalls upstairs; several counters do a plate and a glass of wine standing up.

About half an hour on the purple line from Trindade, which is five minutes from the market.