Budget around USD40 Per night, close to Ben Thanh Market, night life and hopefully quiet by night when we go to bed :)
Very close to the market is Little Saigon Boutique Hotel. It's my go-to recommendation because it is tucked away in a tiny alleyway, and around the corner from L'Usine cafe, where you can get a coffee and breakfast overlooking the chaos below.
Mentioned in this answer:
I spent several night at the An An Hotel. I really liked it - close to the market, close to the river, lots of activity and restaurants.
And just in case you plan to go to Hanoi, I recommend the Hanoi Rendezvous Hotel.