Party at son's place, a cheap lodging (9)
I believe the answer is:
dosshouse
'a cheap lodging' is the definition.
'dosshouse' can be an answer for 'lodging' (dosshouse is a kind of lodging). I am not certain of the 'a cheap' bit.
'party at son's place' is the wordplay.
'party' becomes 'house party' (house party is a kind of party).
'at' is a charade indicator (letters next to each other) (I've seen this in other clues).
'son's place' becomes 'doss' (I am not sure about this - if you are sure you should believe this answer much more).
'house' after 'doss' is 'DOSSHOUSE'.
Can you help me to learn more?
(Another definition for dosshouse that I've seen is " lodging place".)