Vietnam is one of the most incredible countries you can visit in Asia and as it is changing so rapidly, it will be a good move to put it in your bucket list and organize a trip soon. If you are limited in time you can focus on the Northern part of the country where you can enjoy beautiful mountain landscapes while trekking and within one day relax on the beach, enjoying the serene waters of the Pacific Ocean. After spending one month in Vietnam, mainly in the North, I can suggest the following itinerary for your short stay there:
Day 1
If you are travelling by air, buy a return ticket to and from Hanoi. From there you can easily reach the most interesting places in the area. To spend a few days in this incredible city is a must.
Tip: You can check my personal top 10 on what to do in Hanoi here.

A temple in the Old Quarter in Hanoi
Day 2
Spend a full day in Hanoi, then take the night train to Sapa and enjoy the picturesque landscapes and the rice terraces while trekking in the mountain and visiting different mountain villages.
Tip #1: You can plan your Sapa journey using these ideas.
Tip #2: Check with your hotel/hostel if it would be ok to leave your luggage there during the day or even leave part of it there until you come back from Sapa. The staff is used to it so you should be ok. We left our backpack in the hotel for a whole week and they were totally fine with it. A good idea is to book the same hotel/hostel for your stay in Hanoi for your first day there and for the day when you arrive back from Sapa. This way you will not have to carry luggage across the city and lose precious time in search for your accommodation.
Day 3
You will arrive very early in the morning in Lao Cai which is the town with the closest train connection to Sapa town. From there take one of the minivans and travel to Sapa town or the village you will be staying. You will have time for a short trek before it gets dark.
Tip: I recommend you to book accommodation in a homestay in the villages near Sapa town. This will make your adventure much more authentic.
Day 4
Organize one of the longer treks to explore the Sapa valley. It is quite easy to find a guide and arrange a trek with him the day when you arrive. Take the night train back to Hanoi.

A pleasant evening walk in Tavan village in the Sapa valley
Day 5
You will arrive very early in the morning in Hanoi where you can spend the whole day sightseeing.
Day 6
Book a two day-one night Ha Long Bay cruise and just float between thousands of islets. You can either book the cruise in advance or let the hotel in Hanoi arrange it for you. I personally booked it in advance which might be the more expensive option, but the best cruises get fully booked online.
Tip #1: It is essential to book a bit more expensive tour so that you travel with a nice boat, enjoy good service and food on board. Don’t go for the cheapest cruises as most of the people have had terrible experiences with them and this can ruin what can be one of the most incredible experiences in a lifetime.
Tip #2: The cruise companies offer a pickup from the central areas in Hanoi which you need to additionally pay for. Take advantage of it, since this will be the most convenient way to get to the ship.

Ha Long Bay with its thousands of islets and boats packed with tourists
Day 7
You will spend the morning in the emerald waters in Halong Bay and arrive at the marina around noon. Then you can take a boat to get to Cat Ba Island and enjoy a day or two on the beach.
Day 8
Relax on the beach.
Day 9
Get back to Hanoi and spend the rest of the day there.
Day 10
Take your flight back.
Tip: If you are working full time and have a limited number of days off, then this itinerary is a good option as you will need to take only 5 days off (if you skip the 9th day in Hanoi and get back to Hanoi from Cat Ba Island on the 8th day) Book a late Friday or early Saturday flight from your city to Hanoi and then leave early in the morning on Sunday next week, thus you will be able to be back for the busy Monday at work.
Visa on Arrival
Here you can find useful information on obtaining visa on arrival in case you need one.
One month Itinerary Vietnam
In case you have some more time and you want to see more than the above mentioned, then you can check my 1 month itinerary here.