Hungary is a small country with good rail links radiating from Budapest, which makes day trips unusually practical. Most of the following are under two hours each way.
Szentendre — 40 minutes
The easy one. Szentendre is a Serbian Orthodox town of ochre houses and steep lanes on the west bank, settled by refugees from Ottoman advances from the seventeenth century. The old town is small, extremely pretty, and busy at weekends.
The Skanzen, three kilometres north, is the Hungarian Open Air Museum — farmhouses, churches and workshops moved here from villages across the country and rebuilt by region, with a narrow-gauge railway running between them. It is a half-day in itself and it is excellent.
Getting there: H5 HÉV from Batthyány tér, every twenty minutes. A city travelcard plus a cheap supplement beyond the boundary.
The Danube Bend — 1 to 1.5 hours
Visegrád and Esztergom, where the river turns south between hills. Visegrád has a citadel three hundred metres above the water with the best river view in Hungary, and the remains of the royal palace where the 1335 congress of kings was held. Esztergom has the largest church in the country on a bluff over the water, and a bridge you can walk across into Slovakia.
Doing both in a day is possible if you start early. If you must choose: Visegrád for the view, Esztergom for the building.
Getting there: train from Nyugati to Nagymaros-Visegrád and a five-minute ferry, or buses from Újpest-Városkapu. Boats run in summer and take several hours.
Eger — 2 hours
A baroque town in the north-east with a castle that held out against a vastly larger Ottoman army in 1552, a siege every Hungarian schoolchild knows. The minaret in the town centre is the northernmost surviving Ottoman minaret in Europe.
Just outside town is the Szépasszony-völgy, the Valley of the Beautiful Women, where dozens of small wine cellars are cut into the hillside and pour their own. This is the home of Egri Bikavér, Bull’s Blood. Go by train and do not drive.
Getting there: direct trains from Keleti, about two hours.
Lake Balaton — 1.5 to 2 hours
Central Europe’s largest lake, seventy-seven kilometres long, and the Hungarian summer in one place. The south shore is shallow, sandy and family-oriented; the north shore is hillier, with vineyards, the volcanic Badacsony, and the Tihany peninsula with its abbey above the water.
For a day trip, Balatonfüred on the north shore is the most rewarding: a nineteenth-century spa town with a long promenade. It is genuinely worth doing only between May and September.
Getting there: trains from Déli or Kelenföld.
Gödöllő — 45 minutes
The Grassalkovich Palace, a large baroque country house that was the Hungarian residence of Franz Joseph and — more to the point — of Empress Elisabeth, “Sisi”, who loved Hungary and spent as much time here as she could. The apartments are restored, and the story of Sisi’s relationship with Hungary is the thread of the visit.
Getting there: H8 HÉV from Örs vezér tere.
Hollókő — 2 hours
A UNESCO-listed Palóc village of some sixty preserved houses in the northern hills, with a castle above it. It is small and can be seen in two hours, and it is at its best during the Easter festival. Awkward without a car; there are buses from Stadion but they are infrequent.
Vienna — 2.5 hours
Not Hungary, but easily done. Direct Railjet trains from Keleti to Wien Hauptbahnhof run roughly every two hours. Leave early and you have a full day in Vienna, and the contrast with Budapest — a city that kept its imperial money, next to one that lost it — is instructive.
Practical notes
Book Hungarian rail tickets through the MÁV app, which handles English and seat reservations. Intercity trains to Eger and Balaton benefit from a reserved seat in summer.
Most of these are better on a weekday. Szentendre and Balaton in particular are heavily domestic-tourist destinations at weekends.
Choosing between them
If you have one spare day and want the most Hungary for the least effort, take Szentendre and the Skanzen. If you want landscape and a view, take the Danube Bend. If you want to drink well and are not driving, take Eger. If you are travelling in July or August with children, take Balaton.
Practicalities that apply to all of them
Hungarian trains are cheap and generally punctual, and the MÁV app sells tickets in English with seat reservations for intercity services. Reservations are worth having on summer trains to Balaton and Eger.
Sunday services are thinner everywhere, and rural bus timetables in particular drop away sharply at weekends — which matters for Hollókő more than for the rest.
Most of these towns are small enough that everything closes earlier than you expect, museums included, often at four or five. Check closing times before you plan a late-afternoon arrival, and remember that many Hungarian museums close on Mondays.
Finally: almost all of this is doable independently and cheaply on public transport. Organised coach tours to the Danube Bend and Szentendre exist and cost several times the fare, and their main advantage is that somebody else reads the timetable.