Arepas: Corn flour based pancakes, sometimes made with cheese or slightly salted.
Empanadas: The closest comparison would be pastries. These are popular all over South America, so generally each country/region has their own recipe. The filling usually consists of meat, potato, vegetables and rice wrapped in a corn flour crust.
Tamal: Usually eaten for breakfast. A mixture of meat, chicken, potato, vegetables and yellow corn wrapped in plantain leaves and then boiled. Should be accompanied by a large mug of hot chocolate.
Ajiaco: Traditional thick soup based on three kinds of potatoes, chicken, avocado, dairy cream, herbs, corn, among others. Typically from the altiplano region.
Plenty of options. These are only a few and are divided by areas. However, it is very difficult to find a decent Chinese/Japanese restaurant. Do not expect much even if you find any, since most of them are "fake" oriental restaurants.