They probably came "to the gym". No, 'in' would be worse. You could use 'into'.
"At my previous gym, lots of guys used to arrive by 6am." I think this is what you mean.
Note that you can use "okay" (lower case) or "OK" (upper case) but not "ok". Also note that we don't leave a space between a digit and "am" or "pm". It's "6am".