So many cool things exist in Middle-Earth / Arda / Ea and so many cool comments and reasonings have been shared.
Since so many things have come to my mind, especially after reading all of your thoughts, I will take some time to think on this one before I share my wish.
This post will suffice in bumping this thread so I can find it easily.

==========
edited to say
Ok, I am back.
My choice is The Great Elvin Ring Narya
The following is a paraphrase of what I remember of Narya and what I found through research.
Narya was The First Great Elvin Ring made by Celebrimbor. It was adorned with a red stone. The name is derived from the Quenya nár meaning fire. It was also called
Narya the Great,
The Ring of Fire,
and
The Red Ring.
According to text of The Lord of the Rings, Círdan the Shipwright received Narya from Celebrimbor.
In the Third Age, Círdan recognized Gandalf's true nature as one of the Maiar from Valinor and gave him Narya to aid him in his labours.
Narya is described as having the power to inspire others to resist tyranny, domination, and despair ( in other words, evoking hope in others around the wielder ), as well as giving resistance to the weariness of time.
"Take now this Ring," Círdan said to Gandalf; "for thy labours and thy cares will be heavy, but in all it will support thee and defend thee from weariness. For this is the Ring of Fire, and herewith, maybe, thou shalt rekindle hearts to the valour of old in a world that grows chill"
====================
Narya really does seem to be a great gift to have.
To say what I would do with the gift is to say I would love the ability to inspire others to resist tyranny, domination, despair and to able to rekindle hearts.
I would definitely get much joy from that.
Also that it would "give resistance to the weariness of time" seems pretty cool.
"The weariness of time" definitely seemed to be an issue for the undying...The Elves in particular....especially when they loved and or married a mortal.