Through Virginia, coming across inn at first (3)
I believe the answer is:
via
'through' is the definition.
(via means going through)
'virginia coming across inn at first' is the wordplay.
'virginia' becomes 'va' (US state abbreviation).
'coming across' means one lot of letters goes inside another.
'at first' suggests taking the first letters.
The initial letter of 'inn' is 'i'.
'va' going around 'i' is 'VIA'.
(Other definitions for via that I've seen before include "A Roman way" , "Passing through" , "By way of - in Latin" , "By means of" , "Going through" .)