What are they feeing you?
Why am I not surprised that you'd do this? Evil, evil, character!
It's alive and well! Your best bet is to check the Other category in the Party Finder for your whole data center. Most people who open venues (restaurants, clubs, cafes, etc) list there. All you need to do is toss a glamour on and head over. I've done a lot of RP in other games, but am new to the scene in XIV and have found the community to be open and welcome; there's hardly any issue with gatekeeping and Loremeisters I've encountered in other games.
A few tips:
1. Make sure to set your personal boundaries as far as NSFW stuff goes beforehand. I'm married IRL and don't want anything to do with spicy RP so my characters are married. It's a super easy way out that people will respect, if the time ever comes. I honestly haven't encountered any lewd tells or people trying to pick me up at all, even when visiting some of the more racy venues.
2. Come up with a couple simple character story points that you can use as conversation starters and a foundation to build the character on. The whole can't cook proper seafood to save his life is one that I came up with for my character. One or two likes and dislikes, something she's good at, something she's bad at, and one or two past events that are memorable is more than enough to get started without locking you into a super rigid framework. Half the fun of roleplaying is developing your character through interaction with others. Having a basic framework allows for that sort of growth.
3. RP in video games is a cooperative thing and conversation; don't hit people with walls of text. Make sure to give the other person openings to engage you. "Hey, have you checked out the Blue Moon club? I've heard good things.....". "You're from the Black Shroud? I haven't spent much time there, tell me about it...".
Keeping it simple at first and let the other person/people take the lead while injecting things while slowly (over real world time) increasing your interaction is a good way to start. I wish you all the fun in Eorzea!