Esztergom has a handful of good restaurants clustered in the Víziváros district and along the Danube embankment. Most cater to the day-tripper trade from Budapest, which means quality is generally reasonable and opening hours are reliable in summer.
Prímás Pince, in a converted wine cellar near the basilica steps, does the full Hungarian repertoire — goulash, stuffed peppers, duck liver — at prices that reflect its location near the main tourist draw. The riverside terrace restaurants along Batthyány Lajos utca are better situated, with views across the Danube to Slovakia. For something lighter, the market hall near the main square has fresh bread, cheese, and cured meats at local prices.