I have to be honest in that when I visit a country for the first time, I want to know first of all what are their local foods and what are their local drinks. I absolutely hate going anywhere and being presented with food that I can easily get at home. I want to eat what the local people eat, I want to drink what the local people drink. Otherwise, I could have stayed at home and saved a fortune!
Secondly, I want to see the sights off the beaten track. I am not remotely interested in sandy beaches (unless I can fish them), or sunny verandahs - even though that is something I can most definitely not get at home! I want to see the out of the way villages, meet the local people and learn something of the culture I am visiting.
Ancient objects would definitely come in to my enjoyment of a new culture.
History of any place spikes my interest. I enjoy learning about older areas and their historical value. Also, ghosts. I dig haunted places, from afar anyway. I do NOT want to visit any actual haunted areas because I am a chicken.