Still looking for other contenders, but I'm thinking the loneliest (most isolated) Clinton precinct in the country might be a Hispanic neighborhood in Scottsbluff NE? Nearest Clinton precinct is 100 miles away (1 hr 37 min drive) in Cheyenne WY. Can anyone find one more isolated?

I honestly thought I would be able to find a precinct more isolated than just 100 miles, but even in deep red areas you tend to get a Clinton precinct every now & then in town centers or in pockets with high minority populations. NYT precinct map here: https://www.nytimes.com/interactive/2018/upshot/election-2016-voting-precinct-maps.html#10.80/41.865/-103.631/56768

A new contender, the aptly named town of "Jackpot, NV"! Located on the ID border, it went Clinton by 4 votes. The nearest Dem precincts by driving are in West Wendover NV (also very isolated) on the UT border, 124 miles (1 hour & 52 minutes) away!
https://twitter.com/N_Boyajian/status/1322040485913993217

Jackpot was founded when ID banned casino gaming in 1954, leading "Cactus Pete" Piersanti to found Jackpot Jackpot. NV is 56% Hispanic, & West Wendover NV is 57% Hispanic. The other contender for most isolated Clinton precinct, in Scottsbluff NE, was also a majority Hispanic area

1 more contender for most isolated Dem precinct is in the Upper Penninsula of MI, but it's complicated by Mackinas Island, located 40 miles away (not drivable to), which went Clinton. In fact, there is an archipelago of literal Clinton islands in upper MI:
https://twitter.com/N_Boyajian/status/1322047779225690112