Small place initially without facilities for skating? Not quite - touches here and there (9)

'initially without facilities for skating? not quite touches here and there' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.

'small place' is the wordplay.
I cannot really see how this works, but
'small' could be 's' (abbreviation - e.g. clothes size) and 's' is located in the answer.
'place' could be 'rink' (I have seen 'place of curlers' mean 'rink' so perhaps 'place' could also mean 'rink') and 'rink' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?