In Eger you can reach most of its attractions on foot. But you probably cannot do all of them in a single day, so you have to pick and choose, if you have only one day. Don't miss the 700- year old Castle of Eger with its historic museum and a beautiful panorama of the town.
Down in the the main square, Dobó Square, the Turkish minaret and the Basilica are the must-see sights. Also worth visiting the episcopal cellar system under the town, called the "Town under the town."
You can find nice traditional restaurants and confectionaries all over the downtown as well as hotels and guest-houses. Don't forget to taste the world-famous red wine of Eger, called Bull's Blood (Bikavér), but do look out for the higher quality or award winning ones.
At the western edge of Eger there's a wine-haven known as the Valley of the Beautiful Woman (Szépasszony-völgy), where you can visit wine cellars and take a look at the grape plantations, and do more than a little wine tasting. (But remember that Hungary has a zero-tolerance law regarding drink driving, so make sure your driver is not partaking!
Eger is 138 km from Budapest, on motorway M3.