Never use it, but let the whole world know about it, and watch my enemies very carefully leave me alone for the rest of my life. Having a one-use favor from a deity is like having a nuke -- since it's one-use, it's at its most powerful if you never use it, but maintain the constant threat of using it if something irritates you enough.
The only problem with that strategy is the clingers-on who fully intend to try to get me to use that favor on them or something important to them. I'd have to put myself somewhere relatively difficult to access just to cut down on favor-seekers, and that takes a lot of the fun out of it.
Other than that, my life would probably somewhat resemble Mark Twain's "the 1,000,000 bank note" in that my best asset is something I can't use to meet daily needs, but makes daily needs far easier to obtain anyway.