May I ask why you dont want to level another job? One of the appeals of this game is that you can level mutliple jobs after all! You might actually happen to enjoy one of them on occassion - when I first started playing more than 4 years ago I couldnt imagine playing anything but my paladin - and I didnt for the first couple of months. Today I really enjoy switching between the tanks, my scholar, my bard and my redmage - and I at least enjoyed doing all of the job-questlines.

Besides that... the game offers several more or less grindy things to keep you busy:
- Beast Tribes - offering unique questlines, pets, mounts and vendors (mainly for dyes and some crafting products)
- Old Relic-Quests - while not relevant progression-wise anymore, you might wanna do them if you like the looks of the weapon. At least ARR-WAR-relics look pretty cool
- Primal-Mount farming - for ponies, birds and now dogs!
- Crafting/Gathering - even though you mentioned you're not into it, you also asked how "we" are keeping busy... well, I do so by crafting. You could always just level up CUL and a few classes for cross-class-skills and start providing food for your static!
- PvP - yes, you mentioned that and yes, queuetimes can be aweful, but just have the game running in the background while doing something else (reading a book, playing a game on a handheld... personally, I'm cross stitching)
- Maps - my FC is doing map-parties ever so often! Mainly because we need to get them out of our inventories, finally... keeps you busy for a whole evening and with voice chat it is actually entertaining
- Housing and Gardening - granted, not available to everyone, but I can spend a lot of time changing decoration or planning out what to crossbreed next!
- Palace of the Dead - all the way to 200! You could try to solo it - but you could also form a second, mini-static of 4 people to get there! Still challenge enough!
- Re-running Alexander and Coil-Raids - obviously synched and maybe even ilvl-synched. That would require you to find people who'd enjoy the challenge of those fights and arent excatly in for the rewards ofc.

...and an aweful lot of little things like: Khloes WT book, the fashion report, Triple Triad, finding the right glamour, farming for a certain piece of gear or a minion from a dungeon, weekly turn ins for Naago and Zhloe...
Sometimes I play more, sometimes I play less - depending on my mood, basically.
But I feel the worst thing people can do is limit themself by not exploring the options this game is offering - specially in regards to leveling different classes. Getting my monk and dragoon up to 50 back in ARR helped me a lot to become a better tank because I understood the needs of those jobs better. Leveling a healer helped me feeling more comfortable with my HP being closer to 40% than 80% for most of the time. And I ended up actually enjoying bard!
So... if you want to play the game but dont know what to do... my best advice would be to either try out a different job/role or peak your head into crafting!