I'll add more categories:
Closest stretch of Interstate in either direction: Not sure, since I don't keep track at that level of detail, but my best guess would be part of northbound I-985 near Gainesville (~40 miles away).
Closest exit: I don't think I've ever had occasion to use exit 40 on I-285 (3 miles away). If it's not that, it's I-20's exit 66 (~5 miles).
Closest freeway of any type: The freeway portion of Sugarloaf Pkwy in Lawrenceville (21 miles). Closest state-maintained would be the southwest part of the Athens perimeter (49 miles).
Closest town not set foot in: Clarkston (~3 miles)
Closest town never in at all: Pine Lake (5 miles)
Closest 3di: I-124, if it still exists (105 miles). Otherwise I-385 (133 miles), just barely beating out I-459 (136 miles).
Closest numbered state border crossing: A rough tie between US 78's and GA 166's crossings into Alabama (both 61 miles).
Closest Interstate I have traveled none of: I-124 or I-385 (see above)
Closest US route I have traveled none of: US 378 (91 miles)
Closes state route I have traveled none of: GA 3 Connector in Marietta (17 miles). Closest mainline route is GA 360 (19 miles).
I'll add some new ones of my own.
Closest 2di I have never been on at all: I-22 (146 miles)
Closest 3di I have never been on at all: see above
Interstates in my home state I have never been on at all: None.
Interstates in my home state I have yet to clinch in said state: None. In my previous home state, Maryland, I'm missing just the half-mile or so of I-70 between I-68 and the Pennsylvania line.
Unclinched mainline US route in my home state I am closest to clinching in said state: By raw mileage, it's actually US 378 - I haven't been on it at all, but Georgia's segment is only a little over 20 miles. By percentage, probably US 78 (clinched from Temple to Lexington).