This has been something I personally would love to see, and I've seen a few of these topics pop up on Reddit, so I'm definitely not alone.
A personal social space, like an apartment in The Last City or The Tower. Something we can customize, decorate. Maybe we can use some of those overabundant materials and glimmer to sink into getting things to customize. Phantasy Star Online has been doing this for at least two generations and it's a pretty cool thing to have. Just something we can bring our fire team to that can't be accessed by the public without an invite.
Barring personal social spaces for everyone, a space that we can purchase to house our Clans in-game would be amazing. Right now it really feels like Clans aren't living up to their full potential in-game, as so far the only in-game impact is having a Clan tag in your emblem and getting trophies/achievements for doing certain activities with just your Clan. A Clan space would be a great addition, especially if we can have quest-lines that are delivered exclusively to clans for group rewards.
Another suggestion that I came up with to work in tandem with personal/clan social spaces would be to turn weapons and armor we no longer wish to use but would still like to show off into trophies to put up on display in these personal social spaces. We all have weapons and armor we've gotten from raids or missions that we fought long and hard for that we wish not to get rid of, even if we personally don't use them because of our play styles. And I would love to be able to show off maybe some of my Crota's End weapons on a mantle, or raid gear sets in a display case or lining a hallway like medieval armor displays.
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Oh and of course, comment on your thoughts, opinions, or suggestions related to personal/clan spaces on top of voting in the poll. Do you think the trophy idea is good or bad? Honestly I would also be down for Factions in the game to have their own social space as well, if you decide to devote yourself to one faction. I would love to see that turn into a full-out faction war in a later story expansion that links story and PVP together.