I suggest :
1. Hanoi: The Capital City of Vietnam . History is reflected in its temples and architecture and the center of the city has some historic monuments. The Hoam Kien Lake is also feast to the eye.
2. Saigon: It is the economic capital of Vietnam with Giac Lam Pagoda, Reunification Palace, Notre Dame Cathedral with its neo-Roman architecture and for those interested in War History, the Museum.
3. Dalat:
-The Hang Nga Guesthouse & Art Gallery, dubbed by locals as The Crazy House, is a must see. It was designed by Mrs. Dang Viet Nga, and defies popular cultural concepts. The main building resembles Dungeons & Dragons. The rooms are all oddly shaped and the stairways twist and turn. The ceilings are low and the beds oddly shaped and interestingly each room has an animal theme.
-Emperor Bao Dai's Summer Palace is filled with interesting artifacts and works of art, which makes it worth a visit.
4. Nha Trang:Long Son Pagoda. A little further north (1.2 miles) are the Cham Towers of Po Nagar. They were built between the 7th and 12th centuries on ground that was used by Hindu worshippers in the 2nd century.
A good source of info is : http://www.vietnamtourism.com/e_pages/news/index.asp
Of course much depends on your own taste:
From picturesque mountainous regions (in the North)
to awesome beaches (West and South).
From noisy and overcrowded metropolis (Saigon and Hanoi) to relaxed towns (Hoi An).
World Heritage sites, historical places, religious monuments, local markets, its people,..
More sites:
http://en.wikipedia.org/wiki/Vietnam
http://www.virtourist.com/asia/vietnam/index.html
http://www.sino.net/vietnam-tourist-guides/attractions.html