If you live in district 2 or district 7, it is pretty nice to ride a bike there, and it is also better for the earth. So here are where to get a bicycle if you plan to buy one.
Check the Facebook groups
You can find secondhand bicycles on Facebook, at very good price (from 500,000-1,500,000 VND). You should have a look at Buy & Sell in Saigon, and all the groups named Thao Dien and An Phu Neighbour. You can also just post, saying you are looking for a bike, you will see people quickly answering you.
The boutique is on 107 Vo Thi Sau street in district 3. They have a very large choice of bikes, for kids and adults, also for tall people.
You can expect to pay roughly 2,800,000 VND for one bike, similar to this on the picture. They deliver for free but cannot be right away, it is usually the day after you have ordered and paid. The bike comes with a basket, you can ask them to take it off and buy a nice one on Lazada for 300,000 VND like the one the picture. This one is convenient because you can easily put it on and off.
The Bike Shop
The place is located on 250 Nguyen Van Huong street in district 2, and its choice is more sophisticated. For example, you will find a Momentum for roughly 8,000,000 VND. It is very good bicycle, super light with good finishes (leather, bottle holder, etc.). They also have a great choice of Mountain Bikes.