4
If we are talking about somebody who suspects that he may fall to temptation and have inappropriate thoughts about the immodestly attired women there, it is forbidden. There are numerous issurim involved - gazing at inappropriate things is forbidden by לא תתורו אחרי לבבכם ואחרי עיניכם, and having inappropriate thoughts is forbidden under ונשמרת מכל דבר רע (...
3
TL;DR: best to CYLOR
In an answer titled "Men and Mixed Gyms," dinonline.org writes:
There are two issues with a man going to a mixed gym. The first one is the same a going to a mixed beach- he will see women when they are dressed immodestly. The torah tells us, (Numbers 15-39) “Not to stay after our eyes”, and not to look at woman Included in this is ...
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