You are correct that the federal law does not prohibit sex discrimination in "public accommodations", the category that includes your examples. State laws tend to be more restrictive, see for example Washington's RCW 49.60.215 which declares that
It shall be an unfair practice for any person ... to commit an act
which ... results in any distinction ... except for conditions and
limitations established by law and applicable to all persons,
regardless of race, creed... sexual orientation, sex... PROVIDED, That
behavior or actions constituting a risk to property or other persons
can be grounds for refusal and shall not constitute an unfair
The definitions allow for a few exceptions as to what kind of place is so restricted, most notably a facility "which is by its nature distinctly private", nor "any educational facility, columbarium, crematory, mausoleum, or cemetery operated or maintained by a bona fide religious or sectarian institution". Here is a paper that summarizes the situation with women'-only clubs. For example, New Jersey law has the exception that
nothing herein contained shall be construed to bar any place of public
accommodation which is in its nature reasonably restricted exclusively
to individuals of one sex, and which shall include but not be limited
to any summer camp, day camp or resort camp, bathhouse, dressing room,
swimming pool, gymnasium, comfort station, dispensary, clinic or
hospital, or school or educational institution which is restricted
exclusively to individuals of one sex...
So it depends on the state, but most states prohibit any sex discrimination in public accommodations.