Trying to beat Joey P out for the closest, at .4 miles. It’s an 8-minute walk, according to Google.
I moved from Reno to Tbilisi: 6,763 miles, then moved to Dubai: 7,965 miles
About 5000 miles from Baltimore to Santiago, Chile.
For a while, my parents lived here in Houston, and I lived in various places like
Singapore - app. 10k miles
Jakarta, Indonesia - almost the same
Sydney, Australia - about 8600 miles
8800 miles ish from Sydney to New Orleans, so you must be in Perth. 
I’m currently 11542mi from my father.
But I am also 11510mi from my MIL 
Sadly, I am also 11510mi from my wife 
Parents are deceased and I have been on the move since I went to university. My furthest separation distance would be ~16,000 km ( 9800 miles ) when I moved to Brisbane Australia while they were in Maine.
I am not sure if this counts, but after my parental-units dropped my brother, Grunthos, and me off to work at the Earth Life Observatory, they returned with the Mothership to our home world (RA 4h 35m 55s | Dec 16° 30.558’) which is about 65.23 light years from here.
But, I believe Czarcasm has me beat.
Mine are dead, too. **DrumBum **and I win. 