Run-down spot on outskirts of Dodge City (5)
I believe the answer is:
seedy
'run-down' is the definition.
(I've seen this before)
'spot on outskirts of dodge city' is the wordplay.
'spot' becomes 'see' (both can mean to notice or observe).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'outskirts of dodge city' becomes 'dy' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'see'+'dy'='SEEDY'
Can you help me to learn more?
(Other definitions for seedy that I've seen before include "Shabby and a bit dubious" , "Dilapidated" , "Like some cakes" , "Nasty and squalid" , "Down-at-heel" .)