More interesting and unique missions and story arcs for the Shard would be excellent! Having story arcs that grant a 1 week buff at the end would be cool. I'm talking about 1% - 5% buff to one thing (e.g. Fire/Cold resist, Acc or ToHit, Ranged Def, etc) to represent that the Shard doesn't work the way the rest of the game does. This would incentivize spending some time there semi-regularly.
Grant villain access through Aeon Corp - this is something I would dearly love to see. Does the shard become coop or competitive? I could see some competition w/o going full PvP, say competing for access to missions/contacts/neighborhoods by accruing points for your faction. Vig get Hero points and Rogue get Villain points. All Shard current TFs become full coop. Or just make it a full coop zone.
Leave the gravity geysers alone, they're fine the way they are. If you don't like them buy a jet pack. There are other large zones that people don't gripe for teleportation portals in.
I really like some of the other suggestions - particularly the one where gravity on any given island can be in a different direction that the other islands. Sadly, I don't think the game engine will support that. The other thing that isn't going to happen that I'd like to see is for the islands to drift.