After my answer earlier today I did some "research." Web searches for "Levaquin shelf life" mostly take you to on-line pharmacy sites with no information - but lots of offers to sell you the stuff without a prescription (that I don't recommend). I did find one useful article about Cipro shelf life in Biosecurity and Bioterrorism: Biodefense Strategy, Practice, and Science, Volume 10, Number 2, 2012, pp 182-187. It is in the context of government stockpiles for things like the anthrax scare. It appears from this article that the material does not change into something dangerous with time (some pain medications do) but it does slowly lose its potency. They defined the minimum requirement to be 95% bioavailability of the important stuff and tests showed that 88% of samples had at least 1 year beyond original shelf life, and the average was an additional 66 months. Shelf life does depend on storage conditions. They also quote the Israeli experience. They have sub-selected manufacturers, have controlled storage conditions, and are getting a 10 year storage life.
This is for Cipro, and I do not know if Levaquin is similar, but I am going to use this as a guide.