あなたの国ではどんな食べ物が有名ですか？って英語でなんて言うの？

In order to find out what local foods are popular in one's country, you may ask the following?
What kinds of local dishes are popular in your country?
What food is your country famous for?
What are your country's most famous dishes?
Which foods are most popular with the local people?

keywords: popular- liked and admired by many people.
famous for-known for

The signature dish...is a reference to the the dish" most associated" with a place (or indeed a specific restaurant) Most countries have one:
Italy PASTA. UK Roast Beef. India Curry etc

"What is the signature dish of your country? "

The "national dish" of a country is a meal that the country is well known for. For example, Pelmeni are the national dish of Russia. Korea is well known for bibimbap and kimchi. Vegemite is a famous Australian food. When Westerners hear about Japan, they often think of seafood and sushi.

Native speakers often use the phrase 'most famous' to exaggerate how famous or popular something is. For example, sushi might be Japan's most famous dish compared to all other famous Japanese dishes. You can also interchange the words 'dish' and 'food'.

Well, there is probably a slight difference between what people normally eat and what people would really like to eat. The most common foods and the ones eaten most regularly are those which are not expensive and which are readily available. Such foods are known as 'staple' foods. The first example question is asking about the normal basic food that people eat. In the UK, for example, the response would be: potatoes, fresh vegetables like carrots and cabbage, and chicken, beef or pork.

Many different countries are known for various dishes which over time have come to be known as the national dish. For example, in the UK, one of our national dishes is Fish and Chips, or perhaps you can try a nice roast dinner with roast beef, Yorkshire pudding, gravy and mushy peas. The national dish is the dish that most people associate with the country and most tourists like to try when they visit.

When talking about food all different countries enjoy different types of food so you might want to know what food is good in another country 'what food is your country known for?' this is what everyone associates with your country.
Famous/popular means what alot of people like to eat and enjoy