For those who began watching Alty in the 1960s or 1970s, the big derby was always against Macc (usually involving playing them on Boxing Day and New Year's Day).
Owing to Macc's failure to qualify for the Alliance Premier League for the 1979/80 season, the green slime of Vics emerged to become our bête noire (notably assisted by the heinous Jeff Forshaw).
Macc didn't attain promotion into the then GM Vauxhall Conference until the 1987/88 season.
As regards teams from afar who you loathe, well, any Alty supporter who watched the Robins during the 1970s would surely add Boston United to that particular list of infamy.
Can't argue with any of that.
Of course there was once a brief period where there were six teams from Cheshire in the top tier of Non League football:
Alty, Macc, Vics, Runcorn, Witton and Staly
That will never happen again.