...would be my time in Operation Desert Storm in 1991. I was in Saudi Arabia and Kuwait.

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According to this distance calculator, it's almost 8,000 miles (great circle distance) from Los Angeles (where I lived at the time) to Kuwait City. My unit was actually based in King Khalid Military City, Saudi Arabia and Camp Doha, Kuwait, but Kuwait City will do for distance calculations.

The second farthest would be on our Panama Canal transit cruise from a few years ago. That distance was "only" 3,264 miles from home.

I couldn't get too much farther away from home; the antipodal point (~12,000 miles) from me is in the middle of the Indian Ocean.