I have quit (and returned) before. I never think about the place I'm logging out in, but I do think about the gear. As some silent homage to the friends I've had. I always log out in Ochimusha Kote and Byakko's Haidate.
Now, I'd probably logout @ Mee Deggi since you've got me thinking about it.
When I started the game, I made friends with this Paladin 75 (omg, a 75! right! -that was my reaction since he was the only 75 who visted the LS I was in). His name was Lamal.
He tells me that I need O.kotes. So we go and get them. I'm like mnk45. He's helped me get juji gi already that's how I remembered.
We stayed in this zone for two solid days and went something like 2/8/12 on drops/claims/pops.
I remember being a mnk/war and voking him and getting links and my friend flashing him off me and trying to keep me alive.
Great times.
When I leveled paladin, that same friend and I went to get our parade gorgets. My parade gorget and okotes are still on my mule. If rare/ex wasn't mulable, they'd be in storage til the day SE wipes the servers.
Haidate because more of my best memories in that game are at that cat.
Byakko was the first god I tanked (lion's den right, or rather tiger's den) pld/nin and we had the sata line setup, but the nin co-tank popped him without shadows and deserved to die lol.
So I ended up solo tanking him all the way down until the other tank became unweak, and my friend (the same paladin) sends me a tell says "Dude, you're the best damn tank I've ever seen". Now, I know now exactly where Byakko ranked in the scheme of things, but that meant A TON.
I also have tons of memories with my friends Headache, Xial, and Kaidaa, but none of those can be summed up in single pieces of gear.
When I first heard about Rapture, and assumed, like many others, that it would replace XI, I hoped they'd have some kind of system where you could have statues of your 75 jobs in your mog house in that game. Even if it was just your character model in the AF for that job. I had 6 75s and I imagined them like a trophy room.
Having played "Rapture" recently...just lol.