Belfast is a city you can cross on foot in half an hour, attached to a hinterland you could not exhaust in a fortnight. That mismatch is the entire planning problem. Visitors land with two days, spend both inside the ring of Victorian sandstone around Donegall Square, and leave with an impression of a pleasant small city with very good bars. All of that is true. None of it is why you should get on the plane.
What follows is a ranking, and it is meant seriously: this is the order in which we would defend these things if the trip kept shrinking. Two of them are not strictly in Belfast at all, which is not a dodge. The city has spent its whole modern life as the door to the north-east corner of Ireland, and the coast beyond it is part of what it offers.
1. The shipyard, and everything it left behind
Titanic Belfast takes the arrivals and deserves most of them, but the common mistake is to treat it as one building rather than a district. Budget half a day and walk the whole yard.
The museum sits in an angular, hull-shaped shell on the ground where the Harland and Wolff slipways ran, and its galleries were substantially reworked a few years ago. The strongest rooms are not the ones about the ship. They are the ones about the city: Belfast at the turn of the twentieth century, when linen, rope, tobacco and shipbuilding made this one of the industrial engines of the empire, with the tenements and the mortality figures that went with it. The mocked-up shipyard ride divides people and often carries the longest internal queue; we would not grieve over skipping it.
Outside, free and largely ignored, are the slipways themselves. The plan of the hull is laid out at full scale in the ground, with benches at the height of the ship's decks and the names of those who died in the sinking set into the surface. Standing at the head of the slip gives you the length of the thing in a way no gallery can. Along the quay sits SS Nomadic, the tender that carried first and second-class passengers out to the anchored liner at Cherbourg, restored and billed by its custodians as the last White Star Line vessel afloat. Further on, the Thompson Dry Dock and its Pump House let you walk down onto the dock floor and stand under where the hull sat. The Titanic Hotel occupies Harland and Wolff's old headquarters, and the restored drawing offices are generally open to look at even if you are not staying, though it is worth confirming before you turn up.
Overhead stand Samson and Goliath, the yellow gantry cranes that are now protected monuments, with a working yard beyond them that has changed hands more than once in recent years. Timed tickets for the museum are usual and sell out in summer, so book. It is roughly a twenty-five minute walk from the city centre along the Lagan, or a short ride on the Glider G2.
2. The west of the city, and the walls still standing
The Falls Road and the Shankill Road run roughly parallel, a few hundred metres apart, divided along much of their length by walls, fences and gates that are politely called peace lines. The best known stretch, on Cupar Way, is covered in visitors' signatures. The gates at Lanark Way, which link the two roads, are usually closed overnight. That is the single most useful fact about Belfast's geography, and no museum will teach it to you as fast as ten minutes standing there.
The conventional way in is a black taxi tour, typically ninety minutes to two hours, and the better operators will pair you with drivers from both communities or at least be frank about which one they come from. Done well it is the most valuable thing you will do here. Done badly it is a grievance monologue, so ask what the format is when you book.
You can also go alone. The Glider G1 runs along the Falls Road, and Cultúrlann McAdam Ó Fiaich, the Irish-language arts centre with a café and bookshop, makes a sane anchor point. From there it is a short walk to the International Wall with its rotating political murals, to Bombay Street, rebuilt after it burned in 1969 and backing directly onto the wall behind Clonard Monastery, and across to the Shankill and its memorial garden. Two things to hold onto: the murals change and are painted over, so what you saw in a photograph may be gone; and these are ordinary residential streets where people live. Ask before photographing anyone.