IIRC one of Akasha's stories state that Luna was the last mare Agra married. I imagine both Luna and Agra had relationships with mortals in the past so I'm not saying she was some kinda conquest or anything. Akasha's story then goes on to say that Agra eventually dies, though, due to having lost so many loves in the past that his soul had become too damaged for him to stay immortal, essentially. I imagine the truth being more complicated.
I don't know what Agra might have been but, at a guess, maybe a zebra who perfected alchemical immortality. He could craft living things from nothing, after all. He might have eventually died from a conflict, or maybe he just decided he was tired and didn't enjoy immortality anymore. I dunno.
Getting to the point, maybe Luna would have kept the promise rings they might have exchanged. Probably something made of an impossible alchemical material that constantly shifts and shimmers. I could give it fantastical aspects like that it warms and brightens, radiating love when touched by a powerful alchemist. That, if you look through the ring, you can see echos of Agra's most cherished memories with Luna playing out on the other side of it. That sort of thing. In fact, that memory thing would make it pretty explicit what the ring was for and who it was from.
Other ideas might be a small clay zebra and two small clay alicorns. Something Agra might have made to act as walkie talkies between himself and Celestia and Luna, since he was friends of both. They'd probably have some other fancy traits, translating language or following those they were match with around, etc.
Maybe a window that always shows the unblemished outdoors (filtering out from its view anything artificial), or one that always shows the night sky and can be commanded to magnify its view so as to explore the sky as if through a telescope. These previously being gifts to Agra to have in his cave, so he doesn't forget about the outdoors.
Maybe just letters between the three of them, enchanted to never degrade, each written in the flowing script of either alicorn horn or that of a powerful zebra who'd rather have alchemical ink write for him than raise a hoof.
Or maybe, yes, some kind of plushie of Agra. Though I doubt he'd of made it himself, more likely a pony would have made it at Luna's request were she to want something to remind her of him. I mean, if you're making something soft and fuzzy, why not something soft, fuzzy, warm, and alive? You don't become as powerful as Agra and then skimp on a thoughtful gift.
Relics of the sisters might include any number of things. Celestia's telescope, from which she used to watch over her realm. Luna's pillow, made to help her enter dreamworld faster and more easily travel between ponies' dreams. Luna's gavel, used during her night courts to call ponies into order and which raps upon hard surfaces with a sound like rolling thunder. Celestia's laser pointer, capable of facilitating most excellent magical powerpoints...
That sort of thing.
For something more substantive, though, ANYTHING that could help Akasha find Celestia and Luna.
I probably don’t need to say, but Akasha’s greatest desires are for love, adoration, and notoriety. She wants to become a legend, and a substantive one at that. Not a celebrity, not a role model or otherwise person to aspire towards, but someone that does things worthy of eternal glory, and does them by doing things that are GOOD. She definitely isn’t a fan of infamy.
She wants a story not dissimilar to Eldritch Lore's, only instead of stealing and scheming and murdering and corrupting and destroying souls... she wants to be known as someone who healed people, fixed the world, toppled tyrants, purified curses, and hopefully one day finds a way to restore souls. I know it's goddess-teir magic, but seriously. The prince of New Canterlot's soul was ruined by changelings such that he was a screaming mess when he was dragged back. Emerald, the most powerful being in the world right now bar Elly and Libby, has been weakened by soul-focused attacks and is now pursuing learning soul magic. Akasha, when she tried to do the same, failed entirely. She's tried to experience and understand other forms of magic but she can only get so far.
If, after the game, Akasha could pursue (with or without an alicorn) the magic needed to restore souls, that'd be great. To be able to restore the victims of changelings, maybe even to restore changelings themselves. She might even learn how to restore the alicorn that EL had to destroy in order to get her new body, however little that alicorn might resemble Elite Librarian were the soul transfer to of failed.
And finally, to seek out what happened to Celestia and Luna.
These are the kinds of feats she wants to accomplish. Things that make the world better and yet could never have been accomplished, even piecemeal, by anyone but her.