There is CITY SPA on Pico Blvd at Burnside:
http://www.lacityspa.com/
Used to be called PICO/BURNSIDE BATHS (named for the two cross street) probably from the 1950s - what an old school Russian baths would have been like in a basement of a building in New York or Chicago. Went there one time as PICO/BURNSIDE BATHS with a lot of nudity in the wet area. Then the name change to CITY SPA with multi million dollar renovations - I went once & place lacked the charm it previously had - and wasn't very busy. Web site does say sometimes it is co-ed with swimwear required in the wet area at those times - so check first before going if wanting to be naked with other nude men.
"Stag Night at the Steam Baths" looks like a hoot:
http://www.themave.com/bijou/50/stagnite1.htm
Someone sent me GRAND SPA's web link:
www.grandspala.com
If any of you make it up to San Francisco, be sure to checked out KABUKI SPRINGS AND SPA on Geary - in building at street level with KABUKI THEATERS upstairs - huge pay underground parking facility. One day is men's day and then the next women, with their Tuesdays co-ed & swimwear required that day. Saturday is men's day - best day to be checking it out. Traditional Japanese communal baths - 25 to 35 nude men flopping around the place on Sarurdays:
http://www.kabukisprings.com/content/2/
This is the type of place I am trying to find in LA, hence the original posting on the subject.