If you're out of leves and looking for something to actually do there are still options available.

1.) You can check the notice board next to the leve counter. There will be "items of the day" that each crafting and gathering guild are looking for. You can try to procure those items by either synthing/gathering them or purchasing them from players.

2.) Grab a gathering job and start collecting materials. You can either sell these directly from your inventory, give them to your retainer to sell in the market wards, or keep them for crafting items later.

3.) Sidequests. You may notice quote bubbles with exclamation marks inside of them on your mini-map. These mark NPC's who have a quest available to run. Upon talking to the NPC they'll inform you of what needs to be done and what the requirements are for completion.

4.) Exploration. Since you're a beginner, you may want to go around and grab all the Aetheryte camps. During the CE release I would constantly run "Aetherial Expeditions" where we'd grab a large group of people to grab each of the Aetheryte camps. Nowadays it's not really a necessity but it can still be fun grabbing some of the nodes. While it's true you can be teleported to any camp by anyone, you may still want to grab the camps in your downtime in case you get a party invite to a distant area. On top of that you can attempt to grab the Aetherial nodes which you can't be teleported to at all.

5.) Make sure you are "flagged" for an experience party on what ever battle class you prefer to level if that is what you truly want to do. This way people know how to get a hold of you and potentially grab you to fight monsters they normally would be unable to handle efficiently on their own.

I also like just casually walking around Ul'dah and people watching. Whatever you do it's up to you. Have fun and welcome to Final Fantasy XIV.