I visited in 2002, so some of my advice might be out of date. A lot depends on how long you have as its a big country, about the same length as Italy. Sounds like you’re interested in the war, I’d recommend the tunnels Tokes mentioned plus the ones at Vinh Moc. The ones near Saigon were used by Viet Cong soldiers but the Vinh Moc ones were lived in by ordinary North Vietnamese and make an interesting contrast. The museums in Saigon and Hanoi are good on war related stuff too.
I enjoyed the Presidential Palace in Saigon, great example of '60’s luxury, but like a Bond villain lair. Hanoi is nice, good place to chill have a beer and watch the world go by. The water puppets are a good attraction there.Halong Bay is beautiful and well worth seeing.
I enjoyed the ruined Forbidden City in Hue but it’s pretty run down so not for everyone. Beaches at Nha Trang are good, but a lot of backpacker booze cruises which may or may not be your thing. Finally, a tour of the Mekong delta is interesting, you can see cottage industry sugar factories and other local village life.
Hope you have a good time!