(Just to be clear, I'm NOT looking for sales pitches from realtors, but rather suggestions from people living in the area)
Watch your mail box ... they, like ants and cockroaches show up everywhere.
Actually the closest apartments to Bitexco Financial Tower are actually within the building itself. It is a new multi-use building that opened about 2 years ago.
Unfortunately, as you are looking here for accommodation, it's unlikely your salary would get you even a utility closet there.
The Bitexco Financial Tower is located near the intersection of Ham Nghi and Ton Duc Thanh.
Use to locate it (actually the address is located just off the opening screen move down and to the right).
On Ho Tung Mau (streets are named after Northern VN fallen heroes these days), the street on which the Bitexco Financial Tower is physically located, AND on the street on the 'other' side of the building - Hai Trieu - there are several Standard hotels.
Given it is hotel low season, and low prices, you should be able to land a hotel room for around $10-15 a day. This will allow you to search for more permanent accommodation. Remember to get a monthly deal (VN doesn't have discounts, they call them PROMOTIONS).
I know there are decent, presentable hotels with a few minutes walk of Bitexco. (I can't personally recommend hotels because of conflict of interest).
At least you can eat decent VN food across from the Bitexco Financial Tower at the NHU LAN Restaurant.
Using Diadiem.com - it has a search box (don't put street in the search box) - you can check out addresses.
Foreigners are restrained by police as to where they can stay (other than most hotels) which effectively blocks out a lot of the immediate area.
Between Bitexco and the populated part of Quan 2 (massive land clearance scheme in between) it will take 15-20 minutes by taxi (assume taxi is a $1/kilometre).
Using Diadiem.com look for Thi Sach (just off the top of the opening screen). The block defined by Thi Sach - Hguyen Sieu - Le Thanh Ton and Ngo Van Niem has many apartments and long term hotels. Really friendly area. It would take a 20 minute walk to reach your office.
There is a strip of condo buildings, adjacent to the perfumed canal, in Quan 4 - on Hoang Dieu between Calmette and Khanh Hoi that rent.
In reality, most forms of public transport (including taxis) are less than ideal and you will need to get a licence ('exchange' plus a road test) and a set of wheels to get around on.
The Somerset is in need of a refurbishment, as are many of the highrise buildings in Quan 1.
You will find several tired-looking highrises in the Nguyen Thi Minh Khai and Nam Ky Khoi Nghia area. The rents might well fit your budget but then there's transportation.
Other accommodation can be found in Quan 3.
Before you head over spend time with Craigs List VietNam < >, < > to get a feel for the market. NEVER rent anything unseen.
When you move in most landlords require 2 months security deposit PLUS first months rent. You then get to pay for electricity, cooking gas, parking, management fees and anything else the landlord can dream up. GET RECEIPTS FOR ALL MONEY PAID.
When you find an apartment, go over it with a fine tooth comb (unless you like paying for other peoples damage) and when you find damage have the landlord or sales rep stand next to the problem and take a picture. Also notify the landlord, in writing, of all deficiencies.
Most rental accommodation comes with at least the bare minimum of beds, chairs, table(s), sofa, TV, fridge, stove, etc. If you get lucky some LL even throw in sets of sheets, too. A condo I rent even has a microwave, china wear, pots and pans, flatware (knives and forks), as well - all for USD$400/month in a 5-year old building. There is also inside parking, sundeck and a swimming pool. No good for you as you have no wheels. It is a 10-minute ride from your office!