16 Days in Vietnam 

Our total time was 18 days, but two of those were spent primarily getting to and from Hanoi, so our itinerary in Vietnam was really for 16 days:
-2 days in Hanoi
-3 days (2 nights) cruise in Ha Long Bay
-Back to Hanoi, then night train to Phang Nha
-2 nights in Phang Nha with 2.5 days
-Train to Hue
-2 days in Hue
-Van to Hoi An
-4.5 days in Hoi An
-Night train to Hanoi
-2.5 days in Hanoi before afternoon flight home
If I had it to do over, I might make a couple of changes:
-2 days in Hanoi was good. *We stayed at Ja Cosmo Hotel in the Old Quarter, and liked it very much.
-2 day cruise instead of 3. *We were the only guests who did 2 nights. Everyone else was delivered back to shore the second day, and we were put on a day boat alone with a crew to ourselves. I actually enjoyed this peaceful day of cruising around quieter areas of the bay, including about 6 km of kayaking with two crew members. Mike was a bit bored and would have preferred to spend that day heading to the next destination. So, this would be a matter of preference.
-Maybe add that extra day to Phang Nha? This was a favorite segment of the trip. I recommend staying at Karst Villas, which is on the edge of the small village overlooking fields with water buffalos. It is peaceful and quiet and beautiful. There's a very nice pool, a restaurant with excellent food, and the hosts were super personable and helpful. Wait to book your tours through them; it's easy and less expensive. We did a 9km jungle trek that was one of the toughest things we've ever done. And we did a 7km kayaking tour into Phang Nha cave with a 3km "hike" that was quite challenging. It is possible to walk into the cave and the most spectacular part was accessible on foot, but the kayak trip with bouldering and swimming was an adventure.
-Hue: We enjoyed a tour of historic sites and as a mosaic artist, I was thrilled to discover some unexpected and inspiring picassiette-style mosaic covering a mausoleum and an old palace in the Imperial City.
-Hoi An/Da Nang: drop to 3 days. We visited the Marble Mountains, with Buddhist temples and statues inside of caves; very cool. We did the My Son Sanctuary as an early tour, returning to Hoi An by lunch on our final day before catching the night train in the evening. Mike had clothes and shoes custom made, so it did help to have the 4 days. Hoi An is a lovely little town, but also extremely touristy, and we would have preferred one less day there. After a while, we were just looking for air conditioned places to sit and drink cold beverages to kill time.
-We took the night train back to Hanoi, which took 17 hours. On one hand, we slept on the train instead of paying for a hotel, and we enjoyed seeing the landscape. On the other, we could have spent about the same amount on a flight and gotten an extra half day to do something else.
-What we would have done with the time saved by shortening our Hoi An stay and flying back is to stay in Ninh Binh, probably in the village of Tam Coc. We did a day tour and it is absolutely stunning. I would have enjoyed spending more time there.
-We ended up with an evening and another half day in Hanoi before flying home. If we had stayed in Ninh Binh, we might have extended it so that we got transportation back to Hanoi on the same day we flew home.
So, the main advice I have is to favor Phang Nha and Ninh Binh if you enjoy peaceful settings, beautiful landscapes and physical activity. If you are more of a city person who likes bars and street food, you might be more inclined to favor Hanoi and Hoi An, and maybe even spend a night in Da Nang.
And of course, there are many more places that we weren't able to fit into our itinerary. If you have more time, just use this as a jumping-off point. We had an amazing time. Everyone was very friendly and it was easy to communicate. It's a really unique and beautiful country and Western money goes a long way, so you can do a whole lot with a small budget. Seriously, a beer runs around $1.25-$2. You can get a good meal for about $4. It's not good for the Vietnamese people, who work exceedingly hard for very little, but the money we spend does help them out. I hope you have a chance to visit Vietnam!