Vermont, where there's at least a sentimental love for old school New England Republicans. A majority of local offices are still held by Republicans in VT (like sheriff).
Somewhat of a tangent, but why do you suppose Vermont's local political life has remained Republican? My hunch is that older residents with deep roots in Vermont are more likely to vote in local elections (Same reason why there are STILL some Dixiecrat holdout counties in the Deep South 
).
Not being from the state itself, I can only make an educated guess, but I think it's a couple things. 1) Upper New England (VT, NH, ME) has always seemed to pride itself on being "independent minded," and I think it makes people up here (or at least the very crucial group that is the swing voters) uncomfortable giving a fringe too much power. I know that sounds weird because VT is so liberal now, but I think a lot of older Vermonters feel that way (why they could vote for a GOP governor and Bernie Sanders in the same year). 2) VT has a deeply Republican heritage, and I think given the choice between a moderately liberal GOP (doesn't exist nationally, obviously) and their current Democrats, they'd actually prefer the former, but they're not voting for the current national GOP anytime soon. I think a lot of old Vermonters would give the inverse answer of many old Southerners regarding their politics ("the national GOP 'left me'").
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