... this is a fun one. State route is tough because the network is so much more extensive, and they're often used for local trips and not as memorable. I think I got it, but subject to confirmation later.
State Route: NY 383 south of NY 252/RIT, ~15 miles away
US Route: US 20 between I-390 and Bloomfield, ~22 miles away
Interstate: I-86 between NY 36 and I-390, 76 miles away I-481 north of I-90, ~70 miles away
Not much has changed here, other than an answer I had incorrect before.
Adding my answers to some of the other categories:
Closest exit: NY 390 Exit 25 - Vintage Ln (~10 miles)
Closest Interstate exit: I-490 Exit 1 - NY 19 (~25 miles)
Closest freeway of any type: NY 690 north of NY 370 (~55 miles)
Closet 2di segment: My (incorrect) previous overall answer: I-86 between NY 36 and I-390 (~75 miles)
Closest 3di segment: Same as above: I-481 north of I-90 (~70 miles)
Closest overall 2di: Very close race between I-68 (~240 miles) and I-91 (~250 miles)
Closest overall 3di: I-781 NY (~115 miles)
Home state 2di's, never been on: none
Home state 3di's, never been on: I-678, I-781, I-787, I-890, I-295, I-495, I-695
Home state interstates, unclinched: I-84, I-86, I-87, I-88, I-90 (only missing free I-90 in Albany), I-95, I-278, I-678, I-781, I-684, I-787, I-890, I-295, I-495, I-695
Closest overall US Route: US 4 (~190 miles)
Closest overall State Route: Tough, but having recently crossed off NY 246 and NY 262, I
think it's NY 90 (~40 miles)
Closest numbered state border crossing: NY 36/PA 249