Mirage is meant to be a good club, to be honest I've not tried any of the strip clubs (called cabaret bars sometimes here) so can't comment from personal experience
Lots of places in limmasol to stay, obviously I don't know your budget but I would recommend looking on booking. Com for holiday apartments instead of hotels, the main tourist area Germasogeia has bars, cafes, restaurants ect and a lot of escorts are in the area so being there may save you in taxis as opposed to being down by the marina
Stay away from a place called carina apartments, that is mostly populated with Russian escorts, great and safe for going to a meet, but awkward if you're actually staying there