The answer as to where to stay depends a good deal on how much you are willing to spend. I always stay on Hong Kong Island, but it is clearly more expensive than Kowloon. I think Hong Kong island has more to offer but it can be reached from Kowloon it just means more travel. The good news is you can take the airport express to the island or you can and should take a Star Ferry across the harbor. The will not only give you a great view of the harbor but also take you back 50-80 years ago to a time when Hong Kong was different. Take a ferry during the day and also again at night. There is no need to take a fancy harbor tour when the traditional Star Ferry will do the trick. BTW if you are going to be in HKG that long, I would also go to Macau. It is just an hour away by fast boat. Macau is Las Vegas on steroids. It has an MGM and a Wyn etc but only bigger and better. But Macau is a separate country- you will need to take your passport in addition to your money. Fares are cheaper if you tell them the time you will be there- specify the exact time of your return for the cheapest price.
On Hong Kong island there are many fine hotels. The Conrad, the Pennisula and the Marriot are but a few of the nice hotels. They are in the Pacific Place shopping area which has every high end store you can think of. I have also stayed at the LeMeridian which is located farther from the center but is an interesting hotel. Mainly I have stayed at the Conrad and the Marriott. One nice feature of Hong Kong (and why you will find out USA infrastructure is extremely outdated and shabby) is that you can take a free shuttle from airport express (the train) to most of the hotels on HKI. You can also check in at airport express, drop off your luggage on your return flight, and then blissfully go on your way for several hours. You literally check in at airport express with your airline; they give you your ticket; they take your luggage and you don't have to worry about it because they will see to it that it gets on your flight- no carting luggage in the airport. Airport express is comfortable and modern and not at all like any other US based train. Buy your ticket in advance or at the airport. There is no need for a taxi.
Once you check in to your hotel, get an taxi card from the office. It writes in Chinese the hotel address and maybe some other destiniations so all you have to do is point to the destination on the card. Don't expect the driver to know English.
Some good destinations are Stanley Market where you can negotiate for items, the funicular up to the peak, and the downtown markets. Go to flyertalk.com and hit the destinations tab and they will inform you of more than you ever wanted to know. They are really good in talking about shopping and getting knock offs on Nathan Road. There is way too much info there to repeat here. Of course, there is always Disney Hong Kong.
If you want to stay on the Kowloon side the IHG hotel is right there on the bay and is expansive too. There are many more search engines for hotels in Asia than the US. Of course there is expedia etc but try Agoda.com. I would definitely use a search engine like Trivago.com to put you in touch with these others sites, but Agoda is a bigee in Asia. For intra asia flights try skyscanner.com but be careful you read the fine print.
As you move out toward the airport the hotels get cheaper. But there are many fine hotels. Getting around may initially be a problem but usually not for long. I have status with most hotel chains so when i travel i like to stay with them. Because of this I usually get a made to order buffet breakfast that lasts me most of the day. So my food costs are minimual. Other hotels may be cheaper initially but when you consider my food costs the high end hotels may actually be cheaper. Incidently try to use the airport lounges- they are much better than those in the US.
Hong Kong is one of my favorite Far East destinations. I have been to VN too but only Hanoi. HKG has many things to see and do. If you have specific questions don't hesitate to PM me.
PS. In VN be careful about using their money. It is a bit confusing because they use so many 0's. The one thing you need to know is that when you leave VN the money you have from VN is almost completely worthless since it is a closed society. Don't leave with VN currency in your pocket. It has no value outside VN.