We spent 3 weeks in Vietnam a few years ago, just Hanoi, Hoi An and Saigon. Nothing is to be avoided, be adventurous and you will be rewarded! Try the street vendors, they will be excited to serve up a dish to a farang as most westerners tend to frequent the fancy restaurants. As an added bonus, learn to play the national card game of tien len and you will be an instant celebrity! Eat from the local markets, they are loud and noisy and interesting and serve the most amazing food. The hawkers at the markets will generally know a few words of English or possibly have a picture menu if you can't speak the incredibly difficult Vietnamese language.
Hanoi - Try the Pho in Hanoi in the North and compare it to what you get as you move further south (or vica versa). It's a completely different beast. Definitely try Bo Kho which is like a beef and vegetable stew based on the French pot-au-feu stew, but there's many varieties of soups that need to be tasted, like Bun Bo Hue. Nem Chua is a fermented pork cube wrapped in banana leaves and served with raw garlic, delicious. Eat Banh Mi a few times - they can be good or average, rarely bad. Bun cha in Hanoi is amazing - rice noodles served with grilled fatty pork and rissoles, with a side of dipping sauce and spring rolls. My daughter still talks of it, and that was 3 years ago. You can hit up the loud, touristy restaurants for Bun Cha, but there's plenty of little ladies grilling pork rissoles in the old quarter - you'll smell it a mile off, and they are far cheaper/tastier! Also try Banh Cuon – rice noodle sheets laced with wood ear mushrooms, fried shallots, herbs, and nuoc cham dipping sauce. Street food anywhere in Hanoi is great.
In Hoi An we found Banh Xeo - little rice pancakes with crispy prawns cooked into them, shell and all. Sounds average, but they were delicious, so tasty. There's also street barbecues away from the river that serve Thit Nuong, little skewers of meat with wet and dry rice paper rolls, greens, and a satay dipping sauce. Take a dry rice paper roll and top it with a wet one, then add some greens and a skewer and roll it up. Once rolled tightly, remove the skewer from the meat, dip it in the satay sauce and eat! Cao Lau is a dish made with noodles, pork, gravy and greens, the noodles having a unique taste and texture, achieved by using water from a well just outside of town. Another dish was White Rose, steamed shrimp dumplings topped with crispy fried garlic and a sweet/sour sauce. Both delicious. Madame Khanh in Hoi An serves up a mean banh mi. At night the street vendors sell these doughy mango peanut ball things, so delicious. If you get a chance and you're looking to splurge, Baby Mustard is a little restaurant between Hoi An an An Bang beach that's really nice.
Saigon had plenty to offer, lots of amazing soups from memory. We also found a little dessert called Xao, which was like a little pancake, filled with sweet sticky rice and beans and topped with coconut. We tried snail soup (bun oc), something different. Definitely try com suon, which is basically a coal barbecued pork chop served on rice with pickled vegetables. Again, street food abounds and don't shy away from anything, as long as it's freshly cooked (which most of it is).
Coffee. Oh. My God. Vietnamese coffee is just the best! And beer is super cheap, if you drink beer.
Have a great trip!