This answer is based upon my friend and my own personal experience, so it may different to more systematic answer.
There are lots of countries that can be considered the best like among Vietnamese, along with them i also include some of the reason why they popular.
Japan: manga - anime culture, food such as sushi and ramen, great quality brand electric good, discipline, devoted culture. Plus after Vietnam open since 90s, Japan has been one of the countries that offer great help. Even though Vietnam currently at the end of Japan fever, there still a great amount of Japan admirers among Vietnamese.
Korea: pop song, television drama, food such as korean bbq, kimbap and kimchi were great hits. Along with Japan, Korea also one of the earlies countries that invest into Vietnam.
USA: in short, Holywood ???? and then their pop culture. A great number of Vietnamese immigrant also contribute greatly to the love of US.
German: great quality good, great work policy.
France: Paris, city of love. Also art and great food.
China: it may surprise many people. But Vietnamese do love China culture, and it is also China that lots of Vietnamese hate the most, due to various reason. It is a love hate relationship that need a deep research to fully understand it, but for now, Vietnamese people do love China literature, television drama and movie, food and song.
Russia: great help, in the past, in the present. Russia culture is not that popular among Vietnamese, even at the greatest height back in 60s 70s. But USSR/ Russia cartoon(few in numbers, but quite good), quality good, technical school and college, and song still hold the heart of many Vietnamese.