Gellért Hill on Foot: A Cave Church, the Citadella and the Riverside Baths

Gellért Hill is a rock of about 235 metres that rises straight from the Buda bank of the Danube, and the same fault that lifted it also pushes hot water up at its foot. That is why a church, a fortress, a monument and a bathhouse all ended up within a short walk of one another.

This walk goes up from the river by the Cave Church, crosses the summit and comes back down to the water at the Rudas Baths and the monument to the saint the hill is named after. The climb is the only hard part. Choose a clear day, because the views are the reason for the middle of the walk.

The big Art Nouveau Gellért Baths, at the foot of the hill, are closed for a long renovation, so you will see only the outside of the building. The Rudas Baths further along are the place to get into the water.

Start at the river end of the hill, by the bridge, where a neo-gothic monastery front is cut into the rock above a terrace with a statue of Saint Stephen. This is the Gellért Hill Cave, a church built inside a natural cave. The Pauline monks, inspired by the rock sanctuary at Lourdes, opened it for worship in 1926.

The story of the place is the reason to go in. In 1951 the communist state police raided the church, walled up the entrance with concrete and imprisoned the monks. The wall came down on 27 August 1989, and the order returned. Inside you walk through a series of rock chambers; one has hardwood carvings by a follower of the order. It is a place of worship, so keep your voice down.

On the embankment below, look at the water near the shore. A flat rock called the Ínség-szikla, the Hunger Rock, shows above the surface only when the Danube drops very low, which has happened in drought years. When it does, it is the sign of a lean season. Most days there is nothing to see, so treat it as a bonus.

From here the way is uphill, so take it slowly.

The wide stone fortress on the summit is the Citadella. The Habsburgs built it after the 1848-49 Hungarian uprising, and its job was to keep watch over Buda and Pest, with guns that could fire on both.

Walk the ramparts rather than just stopping at the gate. From the walls you see the river, the bridges and both halves of the city at once, which makes sense of everything you have read about Buda and Pest being two towns.

In front of the fortress, a bronze woman holds a palm leaf over her head, as if offering it to the whole city. The Liberty Statue was put up in 1947 and is the work of the sculptor Zsigmond Kisfaludi Strobl. The figure is 14 metres tall and stands on a tall stone pedestal, so it is visible from much of Budapest.

It was raised just after the Second World War. Walk around the pedestal and look up at the leaf against the sky; from the front, the river is behind you and the whole of Pest is spread out in front.

Walk downhill and you come out on the embankment by the bridge, at the Rudas Baths. This is the oldest bathhouse of the walk, and it was founded under Ottoman rule: the governor of Buda, Sokollu Mustafa Pasha, had it built in 1571 or 1572. Rooms from that period survive, including an octagonal pool under an Ottoman dome, and the bath reopened after a renovation in 2006.

If you want to swim or soak, this is the place, and it is the closest thing to the old Gellért experience that is open now. Check the bath's own site for the day, because there are sessions for men and women and sessions for everybody, and bring a swimsuit if you plan to go in. If not, look at the stone front, the Ottoman bath in the middle of a modern embankment, and move on.

A few minutes along the embankment, a colonnade and a waterfall frame a bronze bishop, the Saint Gerard Monument, set into the hillside and facing the Elisabeth Bridge. It went up in 1904, with the figure by Gyula Jankovits, and it marks the hill's story: Gerard was an eleventh-century bishop from Venice who was killed in the uprising of 1046, and the traditional account is that he was rolled down the hill in a barrel. The hill took his name.

Stand below the waterfall and look up at the figure. A small figure of a pagan soldier at the foot of the monument is the work of Aladár Gárdos. It is a good place to finish: the hill is behind you, the bridge leads across to Pest and the city centre, and the next bath of the area, the Rác, is further along the same embankment.

The hill gave the walk its sequence: a church in a cave, a fortress, a monument and a bath, each tied to the water or the rock. Come back another time for the Gellért Baths when they reopen, and for the Rác Baths, which are also closed for restoration.

For the other bank, the city's other guides cover Pest, from the Great Market Hall to the Basilica.