Eger is Hungary's most famous wine town, the home of Bull's Blood (Egri Bikavér) and the Valley of the Beautiful Women, with 200 volcanic-rock cellars open to the public.
Tip: From Eger station, walk 10-15 min into town or head straight to Szepasszony-volgy for cellar tastings.
Tokaj is the world's first delimited wine region, a UNESCO heritage zone north-east of Budapest known for Tokaji Aszú sweet wines and serious dry Furmint from villages like Mád.
Tip: Tokaj town is 3 hours by direct train; Mád and Tarcal villages need a taxi from Tokaj station.
Szentendre on the Danube north of Budapest is a baroque arts town with the Szamos marzipan museum, Hungarian bistros on the riverfront and a Saturday craft market, half-hour HEV away.
Tip: HEV from Batthyany ter on the Buda side; town is walkable, no car needed.
Visegrad on the Danube Bend is the medieval royal palace town where Hungary, Bohemia and Poland summit-summoned in 1335, with riverside Hungarian inns and a citadel above.
Tip: Train from Nyugati to Nagymaros, ferry crosses to Visegrad in 5 min; come back by train via Szob.
Lake Balaton is the Hungarian Riviera, with Olaszrizling whites from the Badacsony vineyards and grilled fogas at lakeside restaurants in Balatonfured and Tihany.
Tip: Balatonfured for the lake's spa town; Tihany ferry from Balatonfured port runs Apr-Oct.
Pannonhalma is the 1000-year-old Benedictine archabbey north-west of Budapest where the monks pour their own wines and run a UNESCO-protected cellar, a quiet day trip.
Tip: Train to Györ then bus 23 min to Pannonhalma village; wine cellar tours run Tue to Sun.