Nine days in Ireland and Northern Ireland: the border nobody can point at

A walled Georgian campus in the middle of the city, founded in 1592 and still a working university. The Book of Kells, an illuminated gospel of about the year 800, is displayed in the Old Library, which is midway through a long restoration, so check what is open before you buy.

Nine hectares of Victorian park with a bandstand, a lake and a memorial arch to the Dublin Fusiliers at the north corner. Locals eat lunch on the grass; it is the obvious place to sit down after the Book of Kells queue.

A narrow Victorian bar with mahogany, mirrors and a snug at the front, ten minutes from the green. No music, no screens, and a proper pint takes a couple of minutes to settle, so do not be alarmed when it arrives half full.

Temple Bar is where you will end up if you follow the noise, and it charges accordingly. Walk five minutes south to the streets around South William Street and Fade Street for the same evening at two thirds of the price.

The seat of British administration in Ireland until 1922, handed over to Michael Collins in a ceremony so brief that the best-known thing about it is an argument over whether he was late. The tour covers the medieval undercroft and the Chapel Royal; the State Apartments you walk yourself.

The collection of an American mining millionaire who left it to the Irish state: Qur'ans, Chinese jade books, Japanese scrolls and some of the oldest surviving fragments of the New Testament. Free, in the castle garden, and there is a roof terrace nobody knows about.

The street between the castle and Trinity has cafes serving people who work rather than people on holiday, which shows in both the price and the queue.

The Vikings built a wooden church here around 1030 and the stone one went up in the 1180s, which makes this the oldest building in the city. The crypt is the largest in Ireland and contains, among other things, a mummified cat and rat found in an organ pipe.

A pub claiming a licence back to 1198, low ceilings, a courtyard, and trad sessions most nights. The claim is arguable and the atmosphere is not.

A prison in use from 1796 to 1924, where the leaders of the 1916 Rising were held and fourteen of them shot in the stonebreakers' yard in May 1916. The Victorian east wing is the photograph everyone knows. Online booking only, and it goes fast.

Ireland's modern art collection in the Royal Hospital of 1684, built as a home for old soldiers and modelled on Les Invalides. The formal gardens and the courtyard are free and worth as much of your time as the galleries.

The cafe in the Royal Hospital courtyard is decent and quiet. Otherwise walk ten minutes east along James's Street, where the pubs do proper lunches for people coming off shift.

Seven floors inside a converted fermentation plant at St James's Gate, where Arthur Guinness signed a nine thousand year lease in 1759. It is a brand experience rather than a working brewery tour, and the pint at the top in the glass-walled bar is included and genuinely good.

About two and a quarter hours from Dublin Connolly to Belfast Grand Central. Sit on the right for the sea south of Newry and the Mourne Mountains beyond it.

White Portland stone, a copper dome and a baroque swagger that says a great deal about what Belfast thought of itself in 1906. Free tours run daily, the grounds hold a Titanic memorial garden with every victim's name, and the whole thing is best seen from Donegall Square North.

A Romanesque cathedral begun in 1899 and finished in stages ever since, which is why nothing quite matches. The stainless steel Spire of Hope was dropped through the roof in 2007 and rises forty metres above it.

Tiled, mirrored, gas lit and owned by the National Trust, with ten carved wooden snugs down one side that you can still shut yourself into. Order at the bar, take a snug if one is free, and look up at the ceiling.

The lanes north of the cathedral hold most of the good kitchens in Belfast and most of the live music, in old warehouses that were derelict twenty years ago.

Opened in 2012 on the Harland and Wolff slipways, with nine galleries taking you from the linen mills that made the city rich to the inquiry that followed the sinking. The best room is the shipyard ride; the last is the seabed footage, and it is very quiet in there.

The pump house and dock beside the museum has a cafe, and the Titanic Hotel in the old drawing offices does a decent lunch under the roof where the ships were designed.

The last White Star Line ship left afloat anywhere: a 1911 tender built to ferry passengers out to Titanic at Cherbourg, because the harbour there was too shallow for the ship itself. Restored in the dry dock next to the museum, and included on the same ticket.

The two yellow gantry cranes over the old shipyard, Goliath from 1969 and the taller Samson from 1974. They no longer build ships and they are listed as historic monuments, which is a fair summary of the last fifty years here.

Around two hours with a driver from one community or the other, stopping at the murals on both roads and at the peace wall between them. Book the evening before; most operators pick up from the city centre.

A Victorian radial prison opened in 1846 and closed in 1996, with a tunnel under the road to the courthouse opposite so prisoners never saw daylight in between. Self-guided or with a guide; the condemned cell and the gallows are still there.

Botanic Avenue and Stranmillis Road feed the students at Queen's, which means cheap, quick and open all afternoon.

Free, and better than it needs to be: an Egyptian mummy called Takabuti unwrapped in Belfast in 1835, Irish gold, and a floor on the Troubles that does not flinch and does not take a side. Two hours is enough.

The park the museum sits in, laid out in 1828, with a curved cast iron and glass Palm House begun around 1839, one of the earliest of its kind anywhere. Free, and full of students the moment the sun comes out.

A little over two hours from Belfast, changing nothing and doing very little except the last forty minutes. Sit on the right after Coleraine.

Neo-Gothic, finished in 1890 and rebuilt twice after fire and bombing, with stained glass telling the story of the city from the guilds of London that paid for it. The council still meets here and the ground floor is usually open and free.

Two permanent exhibitions in a tower inside the walls: the story of the city from the sixth century monastery onwards, and the wreck of La Trinidad Valencera, an Armada ship that went down in Kinnagoe Bay in 1588 and was dug up by local divers in the 1970s.

Trad sessions most nights of the week, packed by nine, and no stage: the musicians sit at a table in the corner and the room arranges itself around them.

A ruined MacDonnell stronghold on a basalt stack with a sea cave underneath it and a bridge across the gap. Sixteenth century, abandoned by the 1690s, and the source of the story that the kitchen fell into the sea during a storm in 1639.

A working distillery trading on a licence granted in 1608, which makes its claim to be the oldest in the world at least arguable. The tour is short, ends in a tasting, and the triple distilled single malt is nothing like what most people expect Irish whiskey to taste of.

The village has a couple of decent kitchens and the Inn does a proper lunch. Ten minutes north, Portballintrae has a harbour and a chip shop with a view.

Around forty thousand hexagonal basalt columns where a lava flow cooled and cracked about sixty million years ago. The National Trust visitor centre charges; the stones do not, and the cliff path down from the road is free and better anyway. Go after four when the buses leave.

The civil rights movement, the Battle of the Bogside and Bloody Sunday, told from the republican side by the people who were there. It takes about forty five minutes and the objects in the cases belonged to the people on the walls.

A single gable end left standing when the terrace behind it was demolished, painted in January 1969 with the line that gave the area its name. The murals around it were painted over three decades and are still maintained.

Walk back up through Butcher Gate into the walled city. The cafes around the Diamond do a decent breakfast and are two minutes from the bus station.