The OED says:
neck n. ... 7. b. orig. U.S. A narrow stretch of wood, pasture, ice, etc. Now usually in neck of the woods: a settlement in wooded country, or a small or remotely situated community; (hence more generally) a district, neighbourhood, or region. in this neck of the woods: in this vicinity, around here (also used elliptically). Formerly also †neck of timber.
Neck was originally productive in this sense: you could have a neck of land or a neck of marsh or whatever, for example:
1705 John Lowthrop Philosophical Transactions and Collections 414 the Principal parts of Port-Royal, now lie in 4, 6 or 8 Fathom Water. That part which is now ſtanding, is part of the End of that Neck of Land which runs into the Sea
1760 Anno Regni Triceſismo Tertio Georgii II. Regis 28 And whereas there is a certain Iſland, or Neck of Marſh, Meadow and Cripple-land, ſurrounded by Delaware River, Hollanders and Hay Creeks
1863 Robert Ballantyne Fast in the Ice 31 the lane of water along which they were steering was, just ahead of them, stopped by a neck of ice that connected two floe-pieces.
And of course, necks of wood:
1780 A. Young Tour Ireland (Dublin ed.) I. 266 You see three other necks of wood,..generally giving a deep shade.
which came to mean neighbourhood:
1871 M. Schele de Vere Americanisms 178 He will..find his neighborhood designated as a neck of the woods, that being the name applied to any settlement made in the well-wooded parts of the South-west especially.
and the original sense of neck was lost, leaving it fossilized in neck of the woods.