There are 2 bathhouses Downtown LA:
The MIDTOWNE SPA
www.midtowne.com
They do offer a 1/2 price room day - that would be the best weekday to go during the week.
Then KLYT BATHHOUSE
132 E. 4th Street
kind of a dump located in the heart of Skidrow
Have seen the Downtowm YMCA mentioned on some sites but couldn't tell you anything about it since I have never been.