This is a truncated version of the 28-day itinerary. You can see quite a lot in a few weeks and catch the major sights along the coast.
Day 1: Arrive in Hanoi
Get settled somewhere cozy (I recommend the Sofitel Metropole), and then take a walk (or cyclo ride) around the Old Quarter and Hoan Kiem Lake.
Day 2: Hanoi to Lao Cai (Sapa)
Enjoy a morning of touring the main sights in the Hanoi Citadel, including Ho Chi Minh's Mausoleum (before 11am), House, and Museum, and the One-Pillar Pagoda. In the early evening, catch the overnight train for Lao Cai (best on a Victoria sleeper car).
Day 3: Lao Cai to Sapa
Arrive in Lao Cai at 6am and hop on a bus for transfer to Sapa. Check in to your hotel -- I recommend the Topas Ecolodge -- and take an afternoon walk down into the valley lined with rice terraces to the Cat Cat Village, or hire a guide for an all-day hike (after a short jeep ride) from Lao Cai to Ta Van. Alternatively, just take in the little town of Sapa, the rice-terraced valley below, and the central market crowded with Hmong people.
Day 4: Sapa to Bac Ha and back to Hanoi
If it's a Sunday, take a day trip to the market town outside of Lao Cai called Bac Ha, the region's most colorful hilltribe market. Otherwise, plan to spend part of the day trekking (contact Topas or Handspan), and then catch an early evening overnight train from Lao Cai back to Hanoi (factor in the few hours from Bac Ha or Sapa to Lao Cai station).
Day 5: Lao Cai to Hanoi
Arrive at 6am in the capital and take some time to rest in comfy city digs. Explore the Old Quarter and Hoan Kiem, and maybe do a bit of shopping. Catch a show at the Thang Long Water Puppet Theater in the evening, or hit some of the town's fine-dining establishments or nightlife.
Day 6: Hanoi to Halong Bay
Leave early in the morning for a 3-hour drive to the pier at Halong City, and then board an overnight boat in the bay -- best aboard the luxury Emeraude or Halong Ginger; one notch down is Buffalo Tour's Jewel of the Bay or Handspan Tour's Dragon's Pearl. You'll lunch aboard the ship, cruise for a few hours with stops at various cave sites, and then sleep aboard the boat moored in a quiet bay. Itineraries vary, and most include time for kayaking to caves and island lagoons and swimming.
Day 7: Halong Bay to Hanoi and on to Hue
Awake to sunlight reflecting off the high limestone formations of stunning Halong Bay. Most trips include a morning kayak adventure and a few stops before returning to the pier and making the 3-hour road connection to Hanoi. Catch the afternoon (4:30pm) flight from Hanoi to Hue (or overnight in Hanoi and fly in the morning).
Day 8: Hue
Set out on a tour by bicycle or cyclo to the central Hue Citadel and the ruins of the old Imperial City. In the afternoon, you can ride a bike -- though it's slightly far -- or arrange a car to a few sights on the outskirts of town. You can arrange a boat to see the likes of the Thien Mu Pagoda and a few of Hue's many imperial tombs -- best are the tombs of Khai Dinh and Minh Mang Tomb or Tu Duc. In the evening, enjoy dinner at Tropical Garden or Club Garden, and then stroll along the Perfume River near the Trang Tien Bridge.
Day 9: Hue to Hoi An
In the afternoon, leave by car or minivan for Hoi An. Along the way, stop at Lang Co Beach, the overlook at Hai Van Pass, the Cham Museum in Danang, and, time permitting, the Marble Mountains. Overnight in Hoi An. If you arrive before the shops close, place an order for your tailored clothes.
Day 10: Hoi An
Follow Day 13 in the 28-day itinerary, above, hitting the beach or exploring town.
Day 11: Hoi An to Nha Trang (via Danang)
Fly from Danang (via a trip to the Marble Mountains in the morning if you've yet to go) and settle in Nha Trang for a few days of beach time. Rest and relax at the Evason Ana Mandara Resort or one of the many good budget options around.
Day 12: Nha Trang
Enjoy the beach, take a scuba course, hop on an all-day boat trip to outlying islands, or hit the city's few nearby sights (the Po Ngar Cham Towers or the Alexandre Yersin Museum). Morning trips to the city market or the fish market near the Po Ngar Cham Towers are popular for photographers. But don't feel pressed -- Nha Trang is a place to kick back, eat good seafood, and rest.
Day 13: Nha Trang to Ho Chi Minh City
You might consider adding a few days at this point and scoot up to the temperate hill town of Dalat or tour part of the Central Highlands. Otherwise, fly to Ho Chi Minh City.
Day 14: Ho Chi Minh City
In the morning, get an early start at Giac Lam Pagoda, Ho Chi Minh City's oldest, and then tour Chinatown and some temples, as well as the large Chinese market, Binh Te Market (all in far-off District 5), before returning to the city center and Ben Thanh Market -- a good place to wander and pick up a few ditties. Stop for lunch at Pho 2000, just adjacent to the market. Time permitting, hit the War Remnants Museum or the Reunification Palace. Enjoy a meal at Quan An Ngon Restaurant, Vietnam's finest purveyor of authentic Vietnamese cuisine in an authentic local setting (there are lots of gussied-up high-end Vietnamese restaurants in town, but funky Ngon takes the cake). Depart.
Going South to North
Note: If arriving in the south (most likely in Ho Chi Minh City), you can reverse this 2-week itinerary. Many travelers include a trip to the Mekong Delta, staying 1 night in Can Tho and exploring the river markets in the area instead of going to Sapa in the far north.