Different Aspects of the Game Besides Combat!

[PandaMonium]

Two other main jobs areas would be Crafting (DoH) and Gathering (DoL), that are 11 more jobs you can level to 70 and maybe enjoy a lot as a good change from fighting.

Logs: there are a lot of kinds of logs you can complete for XP, achievements or just for fun:

Hunting log for every battle job

Grand Company log - you will have to complete it to achieve higher ranks in your GC and to unlock your Squadron

Fishing/ Gathering log - find and obtain all the possible resources

Crafting log - if you are an accomplisher, there are thousand of recipes to obtain and craft - gear, minions, cloths for glamour, furniture and house improvements.

Sightseeing log - discover some most beautiful places of Eorzia that you would never see otherwise.

Get you own house: it may be a long term goal if you are into decorating and such. People are spending hundred of hours playing around their houses or just hanging out with friend there. There are a lot of forum threads and even sites dedicated to housing. Like this for example.
To achieve this goal you might check how to earn a lot of gil, how to play on the Market Board, what crafting jobs to focus to get the furniture you like and so on.

Gold Saucer: welcome to FFXIV Las Vegas! All sorts of mini games, card games and even Chocobo races you can participate in.

Treasure hunt: buy or gather treasure maps and dig shining treasures with your friends

FFXIV has a huge amount of things to do, absolutely huge. I'm playing about 8 months and don't think I saw even 50% of it
So good luck in your journey!