Bad time touring the East Central district (5)
I believe the answer is:
decay
'district' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'bad time touring the east central' is the wordplay.
'bad time' becomes 'day' (day is a kind of time. I am not sure about the 'bad' bit.).
'touring' indicates putting letters inside (touring can mean going round).
'the east' becomes 'E' ('E' can be a synonym of 'east').
'central' becomes 'c' (common abbreviation in various government acronyms).
'e'+'c'='ec'
'day' going around 'ec' is 'DECAY'.
Can you help me to learn more?
(Other definitions for decay that I've seen before include "Go bad" , "Briefly fashionable" , "Putrefaction" , "Deterioration" , "Rot, moulder" .)