Take a river tour - there are various options in the evening, but this time of the year, you are unlikely to see the lights. Or check out the Anonymous statue - think its the dude from Assassins creed myself or the Miniverse - all the history of Hungry in small models
Castle Hill Area
Turkish Baths
They have a rich culinary history (kind of French influenced) and there are many good restaurants. Foie Gras based dishes feature on many menus as well as various incarnations of Goulash.The Central Market Hall is also worth a visit if you are a foodie.