Thứ Sáu

7 days through Vietnam

While our country is small, getting around is not that easy because of the inefficient traffic system (not many highway, no high speed train system). So I really advice you start from Da Nang, then end in Ho Chi Minh. Northern part of Vietnam can wait.

Da Nang is a nice beach city. Unfortunately I'm not from Danang so I'm not sure of the local attractions. But one thing I know is that you should visit Hoian, which is a short ride a way. It's a pretty little town with old architecture that is typical of the 18th, 19th century in Vietnam. It's also famous for silk and is one of the tourist attractions that are better preserved.
7 days through Vietnam
Further North of Danang is Hue (you can take bus or train there, both takes couple of hours). It's the old capital and still has the citadels, royal tombs and other interesting sites. I personally like it a lot for the culture, which is very distinctive from the rest of Vietnam: it's gentle, humble and friendly (that's not to say the rest of us are hooligans!). You'll know when you get there. Remember to check out the cuisine (I love the desserts!).
Ho Chi Minh city, on the other hand, has a upbeat, modern lifestyle with lots of bars, restaurants and entertainment. It is previously known as Saigon before 1975. It portrays Vietnam's modern history with many museums and sites that were used in the were (visit the Cu Chi tunnel!). It would put a nice ending to your trip: A mix of old and new, representing how the country is changing.

As other people pointed out here, 7 days is too short for travel around Vietnam. So IMHO, you shouldn't try to accomplish it. I will list out some route you may interested in here:

1. Northern 
From Hanoi (1 day) --> Ha Long(1.5 day) --> Hanoi(0.5 day) --> Sapa(2 days) --> Ninh Binh (1 day) --> Perfume Pagoda(0.5 day) --> Hanoi (0.5 day)

2. Northern 
Hanoi --> Moc Chau --> Mù Căng Chải --> Ô Quy Hồ --> Sapa -->Lao Cai -->Ha Giang --> Hanoi (This route is more suitable for biker)

3. Central Vietnam
Hue (2 days) --> Da Nang (1-2 days) --> Hoi An (1 day) --> Nha Trang (1 days) --> Ho Chi Minh City or Hanoi (1 days)

4. Southern Central Vietnam
Ho Chi Minh City(1 day) --> Vung Tau(1 day)--> Ke Ga, Phan Thiet, Mui Ne (2 days) --> Nha Trang (2 days) --> Ho Chi Minh City(1 day)

5. Mekong Delta
Ho Chi Minh City (1 day) – Tien Giang (0.5 day) – Ben Tre (0.5 day) – Can Tho (2 days) --> Tra Vinh (1-2 day) --> Ho Chi Minh City (1 day)

6. Southern and Island
Ho Chi Minh City(1 day) --> Can Tho (2 days)--> Ca Mau(1 day) --> Phu Quoc island (2 days) --> Ho Chi Minh City (1 day)

7. Central Highlands
Ho Chi Minh(1 day) --> Bao Loc (1 day) --> Dalat (2 day) --> Buon Me Thuoc (1 day) --> Pleiku (1 day) --> Ho Chi Minh (1 day)

There are other routes but they are not easy for first-time visitor so I don't mention. The time in each place above include travel time. You should take a look on the place I mentioned and choice one before setup for more detailed plan.

If you need more information, please comment/message me.