Many fans will have a view on this and there are quite a few to choose from.
Three that spring to mind are:
3 consecutive FA Cup third round pairings away to Leeds in 1956,57 and 58, all ending 2-1 to City.
Finishing runners up to Huddersfield in the 1924-25 First Division on the same points and goal difference. Using today's formula, we would have clinched the title on most goals scored.
My personal favourite....finishing bottom of the 1st Division in the 1928-29 season, having conceded the fewest goals in the division. The team directly above us (Bury) conceded 40 more !