Try these:
A & Em Hotel http://www.hotels-in-vietnam.com/hotels/saigon/A&Em5_hotel.html
New Star Hotel http://newstarhotel.com.vn/index_e.html
A & Em is a little cheaper with rooms starting at $42 (with little slit windows) but they are currently doing construction on the ground floor so be sure to request a room on one of the upper floors if you end up there.
I thought New Star was nicer but the rooms start at $50.
On the other end of the spectrum, try Sao Nam Hotel in the backpacker district. Rooms for $15-20 (with a discount for stays longer than 3 days I believe). Extremely no-frills but clean rooms.
Sao Nam: #175/5 Pham Ngu Lao T9206472, soouthernstar@yahoo.com.vn