Things to do in game....

[Ovenmitts]

The character you linked is lacking mounts. And as a massive proponent to mounts, I would suggest you gear up a main class and try clearing extreme primal content. You have ARR, HW, SB, and the 2 current ShB EX primals to go through for mounts. I posted the pics in another forum that has since... vanished, but they are all quite pretty and glowy. You'd enjoy them! You said you are not interested but you should definitely give them a chance.

You can run daily PVP to tally up wins for PVP ponies and ADS mounts.

You can participate in scheduled Diadem runs to work toward a pegasus mount and achievements/title. Check this forum out for the discord link. Please note that since ShB hype has not died down, Diadem runs have thusly also slowed but will most likely gain more interest as soon as the current content has had a few weeks in the limelight.

You can play Deep Dungeon, a roguelite, which includes Palace of the Dead and Heaven on High for the achievement and potential mount drops from the sacks obtained from within the duty. PotD has the black and red pegasus and Heaven has the dodo. Get 3 people together with yourself and climb to the peak! Or, simply farm for quick exp.

You can run savage content for mounts (minion during Midas only). Older savages can be unsynced, so if you're not so into higher end content, you can still profit off the loot and glamz if you post a PF and find 7 or less willing participants.

Gain beast tribe reputation in order to unlock new items in their own unique stores, which includes access to buying each tribe's unique mount.

Level a 70+ class in ShB fates with a party of at least 2 for the market achievements to unlock gem traders that can give you craft mats, minions, music, etc. TBD if they will do anything else but I like this experimental feature.

Level DoH/DoL to play the markets and make money. Warning: may take considerable amounts of time facerolling or accessing levekits from FCs or randoms. Not my favorite activity which is why I'm a hobo.

Start a relic quest chain for each expansion. ARR begins in the Shroud and will take you through old content farming for atma, light, and so on. HW will bring you to Azys Lla and ask the same of you. SB will introduce you to a new world called Eureka, which can get you some seriously cool mounts all at the cost of massive facerolling. You may need to join a revival scene in order to do this content since I'm sure it has died down massively. Still, I did really like the Baldesion Arsenal when that was the new hotness. I really enjoyed the sense of adventure. Worth the time investment imo but your millage may vary, and it will depend on how many other people are in the zone for success.

Level 1 DPS, 1 healer, and 1 tank to 80 to unlock Mentor Roulette for a shot at filling queues in content no one wants to do anymore. Be sensible and don't say anything stupid since you are here to satisfy their thirst for adventure and to get a win added to your 2000 for a special 2-seater mount.

Climb Kugane Tower for great screenshot and a feeling of accomplishment.

Participate in seasonal events. This month's flavor is beach bums and we will be celebrating the Moonfire Faire!

Do each Sightseeing Log entries for a chance at minions and bragging rights. Warning: ARR's are veeeeeery picky and require very specific weather and time requirements.

...

I can't think of anything else right now but I feel like that's a decent start for a new player. Welcome to FFXIV!

Oh, I forgot. You can also buy/gather specific treasure maps and go treasure hunting. Sometimes even takes you into a new instance that's mostly all RNG, all hype music and drops nice MB sellables.